WO2012034186A1

WO2012034186A1 - Relaying signals in a wireless network

Info

Publication number: WO2012034186A1
Application number: PCT/AU2011/001196
Authority: WO
Inventors: Yonghui Li; Branka Vucetic
Original assignee: The University Of Sydney
Priority date: 2010-09-17
Filing date: 2011-09-16
Publication date: 2012-03-22

Abstract

This disclosure generally concerns wireless relay networks, and in particular, a method for relaying signals between a source node and a destination node in a wireless network. The method is performed at a relay node and comprises: (a) determining a soft input to a soft-input-soft-output encoder based on signals received from the source node, wherein the soft-input-soft-output encoder comprises a linear encoder; (b) using the soft-input-soft-output encoder, encoding the soft input based on a generator sequence of a constituent code to obtain a soft-encoded signal; and (c) transmitting the soft-encoded signal to the destination node. In other aspects, this disclosure also concerns a method for processing signals at a destination node, a destination node operable to perform the method and computer program for implementing the method.

Description

Relaying Signals in a Wireless Network Cross-Reference to Related Applications

The present application claims priority from Australian Provisional Application Nos 2010905216 and 2010904213 , the content of which is incorporated herein by reference.

Technical Field

This disclosure generally concerns wireless relay networks, and in particular, a method for relaying signals between a source node and a destination node in a wireless network. In other aspects, the invention concerns a relay node and computer program for performing the methods. Other aspects include a method for processing signals at a destination node, a destination node operable to perform the method and computer program for implementing the method. Background

In wireless networks, a transmitted signal is overheard by all nodes in the vicinity of the transmitter. Similarly, a receiver can hear transmissions from multiple neighbouring nodes. This broadcast nature of wireless networks provides unique opportunities for collaborative and distributed signal processing techniques. Nodes other than the intended destination can listen to a signal at no additional transmission cost and it is globally efficient for these nodes to forward the information to the destination. This process of transmitting data from source to destination via one or more nodes is referred to as relaying, which has shown to yield spatial diversity and great power savings [1-2].

Two most frequently used relaying protocols in relay networks are amplify and forward (AAF) and decode and forward (DAF) [1-3]. With AAF, a relay node amplifies received signals from the source node and forwards the signals to the destination node subject to the power constraint at the relay node. With DAF, the relay node decodes the received signals from the source node, re-encodes the signals with the same or a different code and forwards the codeword to the destination. Some variations of AAF and DAF protocols include selective DAF (S-DAF) [1], soft information relaying (SIR) [4-8] and adaptive relaying protocol (ARP) [9], In [8], a DTC scheme with soft information relaying (DTC-SIR) has been proposed. Instead of making decisions on the transmitted information symbols at the relay as in other distributed coding schemes [16-18], the relay calculates and forwards the corresponding soft estimates. Some distributed coding schemes have been proposed to exploit the spatial diversity and the distributed coding gains in wireless relay networks [10-17]. By applying the space time coding principle, distributed space time codes [10- 13] have been proposed for wireless relay networks. To further improve the system performance, the distributed LDPC codes [14, 15] and distributed turbo codes (DTC) [16-18] have been developed for a 2-hop single relay network.

Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this application. Summary

According to a first aspect, there is provided a method for relaying signals in a wireless network comprising a source node, a destination node and one or more of the relay nodes, the method being performed at a relay node and comprising:

(a) determining a soft input to a soft-input-soft-output encoder based on signals received from the source node, wherein the soft-input-soft-output encoder comprises a linear encoder;

(b) using the soft-input-soft-output encoder, encoding the soft input based on a generator sequence of a constituent code to obtain a soft-encoded signal; and

(c) transmitting the soft-encoded signal to the destination node.

Using the method, the relay node performs an encoding process before relaying signals received from the source node. Instead of making any hard decoding decision based on the received signals, a soft input is determined and encoded using a soft-input-soft- output encoder. Advantageously, decoding errors are reduced, especially when the link between the source node and the relay node is error-prone and causes decoding errors. In at least one embodiment, the soft input also improves, if not maximises, the signal- to-noise-ratio (SNR) of the encoder's soft-encoded output.

The method is distinguishable from the DAF protocol, which suffers from performance degradation due to error propagation during the decoding and re-encoding process when decoding errors occur at the relay node. Further, unlike existing distributed coding schemes that are based on the DAF protocol, there is no assumption that relay nodes can always decode correctly or will not forward when they cannot decode correctly. Advantageously, the method provides improved coding gains compared because premature hard decisions are avoided at the relay node and error propagation in the re-encoding process is alleviated.

It is also an advantage of the method that a soft-input-soft-output encoder with a simple structure is used for soft encoding. Compared with a non-linear encoder that performs complex and nonlinear probability inference operations during encoding, the method according to the first aspect can be performed using a linear encoder with reduced computational complexity and time.

The soft input may comprise a sequence of soft symbol estimates of information symbols received from the source node, each soft symbol estimate being a posteriori probability (APP) of the corresponding information symbol given the signals received from the source node.

The soft-encoded signal may comprise a sequence of codewords that are each encoded by the soft-input-soft-output encoder as a product of one or more of the soft symbol estimates of the soft input.

The soft-input-soft-output encoder further comprises a logarithm computational module, and a exponential computational module, and step (b) further comprises:

calculating a logarithm of the soft input;

encoding the logarithm of the soft input using the linear encoder based on the generator sequence of the constituent code; and

calculating an exponential of the encoded soft input to obtain the soft-encoded outputs. The soft-input-soft-output encoder uses one of the following linear codes: convolutional coding, block coding, low density generator matrix (LDGM) coding and low density parity check code (LDPC) coding.

Step (c) may further comprise soft decoding the signals received from the source node before step (a) if the received signals are encoded. At the destination node, the soft-encoded signals from multiple relay nodes may be used to form a codeword and decoded to estimate information symbols sent by the source node. In this case, spatial diversity of the plural relay nodes is utilised to further improve coding gain.

The constituent code may be allocated based on an input signal-to-noise-ratio (SNR) value of the soft-input-soft-output encoder and a weight of the generator sequence of the constituent code. According to a second aspect, there is provided a method of processing signals at a destination node in a wireless network comprising a source node, a destination node and one or more relay nodes, the method comprising:

(a) receiving soft-encoded signals relayed by one or more of the relay nodes according to the method of the first aspect;

(b) decoding the one or more received soft-encoded signals to estimate information symbols transmitted by the source node.

According to a third aspect, there is provided a wireless relay system comprising:

(a) a source node operable to broadcast signals;

(b) one of more relay nodes operable to:

determine a soft input to a soft-input-soft-output encoder based on signals received from the source node, the soft-input-soft-output encoder comprising a linear encoder;

using the soft-input-soft-output encoder, encode the soft input based on a generator sequence of a constituent code to obtain a soft-encoded signal; and transmit the soft-encoded signal to the destination node; and (c) a destination node operable to:

receive one or more soft-encoded signals transmitted by the one or more of the relay nodes; and

decode the one or more received soft-encoded signals to estimate information symbols transmitted by the source node.

According to a fourth aspect, there is provided a method for allocating constituent codes to relay nodes in a wireless network comprising a source node, a destination node and the relay nodes, the method comprising: (a) determining a weight of a generator sequence of each of the constituent codes;

(b) determining an input signal-to-noise ratio (SNR) value of each of the relay nodes; and

(c) allocating one of the constituent codes to one of the relay nodes based on the weight of the generator sequence of the constituent code and the SNR value of the relay node, wherein the allocated constituent code is used for soft encoding of signals received at the relay node. Using this allocation method, constituent codes are not used arbitrarily, but rather allocated to relay nodes in the wireless network based on the input SNR values at the relay nodes and the weight of the generator sequence of the constituent codes to improve Bit Error Rate (BER) performance. To further improve, if not maximise, the BER performance, the p-th largest weight of generator sequence to the relay node with the p-th largest input SNR. In this case, in step (c), the constituent code with generator sequence having the largest weight may be allocated to the relay node with the largest SNR value, the constituent code with generator sequence having the second largest weight may be allocated to the relay node with the second largest SNR value, and so on.

Unlike DAF protocols where the error performance degrades as the number of encoder states increases, the performance of one or more embodiments of the allocation method improves as the number of encoder states increases, thereby bringing distributed coding gains compared to compared to SIR-based protocol without relay encoding.

The method may further comprise ordering the input SNR values and the weights in a decreasing order before step (c), and allocating the constituent codes in step (c) based on the ordered weights and input SNR values.

The SNR values may be average SNR values if a wireless channel between the source node and the relay node is an Additive White Gaussian Noise (AWGN) channel. Alternatively, the SNR values may be instantaneous SNR values if a wireless channel between the source node and the relay node is a slow fading channel. The method may further comprise repeating steps (a) to (c) at different time slots. Advantageously, the allocation of constituent codes is updated in real-time based on the instantaneous SNR values of the relay nodes. The relay node may encode a soft input to a soft-input-soft-output encoder based on a generator sequence of the allocated constituent code. In this case, the soft input is determined at the relay node based on signals received from the source node and the soft-input-soft-output encoder comprises a linear encoder. According to a further aspect, there is provided a mobile equipment operable to perform the method according to the first, second or fourth aspect. According to yet a further aspect, there is also provided computer program comprising executable instructions operable to cause a mobile communications equipment to perform the method according to the first, second or fourth aspect.

Brief Description of Drawings

Non-limiting example(s) of the method and system will now be described with reference to the accompanying drawings, in which:

Fig. 1 is a schematic diagram of a wireless relay network.

Fig. 2 is a schematic diagram of the structure of a relay node.

Fig. 3 is a flowchart of steps performed by a relay node for relaying signals from a source node to a destination node in the network in Fig. 1.

Fig. 4 is a schematic diagram of the structure of an encoder at relay node p for an exemplary constituent code.

Fig. 5 is a trellis diagram for the encoder in Fig. 4.

Fig. 6 is a flowchart of steps for allocating constituent codes to relay nodes.

Fig. 7(a) is a plot of frame error rate (FER) for two relays in AWGN channels with Signal to Noise Ratios (SNRs) γ„ = γ„ , = y_{sr 2} -3dB and f_sr = y_rd .

Fig. 7(b) is a plot of FER for 2 relays in AWGN channels with average SNRs y„ = Ϋ„_Λ = y„_t2 -IdB , and γ„ = f_rd +IdB .

Fig. 8(a) is a plot of FER for 2 relays in fading channels, with average SNRs

Fig. 8(b) is a plot of FER for 2 relays in fading channels with average SNRs

Fig. 9(a) is a plot of FER for 3 relays in AWGN with average SNRs fsr =

= f„_j -AdB , 3nd f„ = f _rd . WGN channels, with average SNRs

7sr =

+ 3dB

Fig. 10(a) is a plot of FER for 3 relays in fading channels, with average SNRs

Fig. 10(b) is a plot of FER for 3 relays in fading channels, with SNRs

7s, = YsrA = r,r,2 ,∞<1 7 sr = 7_rd + ^{1 ■}

Detailed Description

Referring first to Fig. 1, the wireless network 100 comprises a source node 110, a destination node 120 and K parallel relay nodes 200 that relay signals between the source node 110 and the destination node 120. A "node" in the network is generally a mobile communications equipment such as a mobile phone or computer operable to receive signals using a receiver (RX); process the received signals using a processor and transmit signals using a transmitter (TX). As such, it should be understood that a source node 110 may also be capable of operating as a relay node and a destination node.

Although a general 2-hop parallel relay network is shown in Fig. 1, the methods disclosed in this description are also applicable to networks with three or more hops. Similar to [1,2,8,9], it is assumed that the source node 1 10 and relay nodes 200 transmit signals over orthogonal channels. Wireless communications among the source 1 10, destination 120 and relay nodes 200 may be implemented using any suitable wireless technology, such as systems based on Time Division Multiple Access (TDMA), Code Division Multiple Access (CDMA) and Orthogonal Frequency Division Multiplexing (OFDM).

In this example, the direct link 130 between the source node 110 and the destination node 120 is considered to be too noisy. The K relay nodes 200 assist the source node 110 to convey information to the destination node 120, thereby increasing network reliability and coverage. However, it will be appreciated that the direct link 130 between the source node 110 and the destination node 120 can be considered if the direct link 130 is not too noisy.

The links 140 between the relay nodes 200 and the source 110 or destination 120 node are known as relay links 140. At the source node 1 10, the binary sequence of length N generated is represented as:

B = (b(\), -,b(k), -,b(N)) ,

where information symbols b(k) for k = 1 ,...,N can be uncoded or coded. B is first modulated into a symbol sequence X_in = (Χ_ίπ(\), · · -, X_m (k), - - - , X_ln(N)) and then transmitted, where X,„(k) is a modulated symbol of b(k) . The modulated symbol X_ln(k) depends on the modulation scheme used.

If Binary Phase Shift Keying (BPSK) is used, symbol 0 and 1 are modulated into +1 and -1 , respectively. The source node 1 10 first broadcasts the signals Xj„, which are received at n parallel relay nodes 200. A time divisional multiplexing scheme, where each node transmits in the separate time slot, is used but other suitable multiplexing schemes such as frequency divisional multiplexing may be used.

As shown in Fig. 2, each relay node 200 comprises a receiver (RX) 210 for receiving signals, a soft decoder 220 for decoding signals, a processing unit 230 for performing calculations and signal processing, a Soft Input Soft Output (SISO) encoder 240 for re- encoding signals and a transmitter or transmit antenna (TX) 250 for transmitting signals. A memory or storage device 260 for storing data is accessible by the soft decoder 220, processing unit 230 and encoder 240.

The method for relaying signals performed by each relay node 200 will now be described with reference to Fig. 3. Throughout this specification, one or more embodiments of the method will also be referred to as a distributed soft coding (DISC) scheme. In step 310, the relay node 200 first receives signals broadcasted by the source node 110 using the receiver 210. At the p-t relay node 200, let Y_r,p ~ { _r,P 0)> _r,p (N)) be the received signals, where:

P_{s p} is the average received signal power at relay p, h„ _p is the fading coefficient between the source and the p-t relay, modelled as a zero-mean unit variance complex Gaussian random variable (RV), n_{r p}(k) is a zero mean complex Gaussian noise with variance of σ„² .

Next, in step 320, the received signals Y_{r p} are decoded by the soft decoder 220. This step and the soft decoder 220 are not necessary when the received signals are uncoded because soft estimates can be calculated directly from the uncoded received signals. The processing unit 230 then calculates a soft input to the SISO encoder 240 based on the decoded signals or the received signals if the decoding step is omitted; see step 330. The soft input is in the form of a sequence of soft symbol estimates (SSEs) X_in(k) of corresponding modulated symbols X_in{k) and information symbols b(k) for k = 1,...,N.

Soft symbol estimate refers to real, non-binary symbol-related information that is not hard decision. It carries the reliability and likelihood information of the source symbol. For example, if a binary symbol b(k) is decoded as 0.8, which means that the decoded symbol is more probable to be 1 rather than 0. Similarly, if the symbol b(k) is decoded as 0.3, it is more likely that it is a 0. Instead of making a hard decision of whether b(k) is a 0 or 1 , the soft input is calculated and provided to the encoder 240 to increase its performance. The soft symbol estimate is then encoded using the SISO encoder 240 at the -th relay node 200 to generate encoded signal x_{r p}(k) , which is transmitted to the destination node 120 by the transmitter 250; see steps 340 and 350. Signal x (k) is generated through a relay function and satisfies the following power constraint:

where P_{r p} is the relay transmission power at the p-t relay node 2 0, x_{r p}(k) is then forwarded to the destination node 120.

At the destination node 120, the corresponding received signal from the p-t relay node 200 for the k-th symbol can be written as:

JO« ⁼ _P^W + ¾, ) (3) where h_{rd p} is the fading coefficient with a zero mean and unit variance of the relay link 140 between p-th relay node 200 and the destination node 120, and n_{d p}{k) is a zero mean complex Gaussian noise with variance of

. The signals y_{d p}{k) forwarded from relay nodes 200 p = \,...J are used to form a codeword and then decoded.

SISO Encoder 240

An exemplary SISO encoder 240 at a relay node 200 will now be described with reference to Fig. 4 and Fig. 5. In this example, the SISO encoder 240 is for a single constituent convolutional code of four states. Constituent is a component code of a channel encoder. A channel code may include a number of constituent codes. Each constituent code has a generator sequence. It should be understood, however, that any other types of linear codes that can be described by a generator sequence can be used, such as such as block codes, low density generator matrix (LDGM) and low density parity check code (LDPC).

A convolutional code generates coded symbols by passing information bits through a linear finite-state shift register that holds some symbols for subsequent calculations. For example, a convolutional code with the encoder generator sequence of g^ps=(l 1 1) and generator matrix G is shown as follows:

In this example, the corresponding weight of the generator sequence g_p =(1 1 1) is 3, as defined by the number of ones in the generator sequence. Throughout this description, the 'weight' of the generator sequence of a constituent code will also be referred to as 'generator sequence weight (GSW)'.

The corresponding structure of the encoder 240 that generates output symbol X(k) is shown in Fig. 4. The encoder 240 comprises a logarithm computational module 242, shift registers 245 and 246, modulo adders 243 and 244, and exponential computational module 248. Let So represents the value of shift register 245 and S I represents the value of shift register 246 at time k, the encoder state can be represented using four states SoSi : S₀(k)= 00,

10 and S₃(k)= 1 1. Given an encoder input at time k, the output of the encoder X(k) depends on the input and values of registers 245 and 246. Let Y, be a vector of received analog signals and B = (b(l), - - - ,b(N)) be information symbols included in the received signals. Denote the a posteriori probability (APP) vector, given Υ_Γ , by

Ρ,^ ί^_οΟ ^Ο)),-.^^)^^)),···,^^)^^))} , (4) where probabilities P₀(k) and P^k) are the APPs of b(k)=0 and b{k)=\ , given Y_r at time /fc. The corresponding trellis diagram in Fig. 5 illustrates the four states of the encoder 240, and the state-dependent outputs and will be explained further below. In this example, given Pjn, the probability inference method in [8] is used to calculate the encoder 240 outputs. Let P(X(k) = w \ ¥_ln) represent the probability of X(k) = w , where w=0, 1 , it follows that [8]:

X(k) =∑ P{X(k) = w I Pjmod(w)

where U(X(k) = w) is the set of branches, whose encoder output is equal to w, w' is the corresponding input symbol; b_k (m, m ^f) represents the input information symbol resulting in the transition from state m ' at time (k- l ) to m at time k, P_{bk im m')} (k) is the probability of information symbol b_k(m, m') at time k and mod(w) is the modulated signal of w. Initially, at time 0, P(S₀(0))=1 and P( 5 (0)) = 0, y^'≠0 . Using Equations (5) and (6) alternatively, the following can be obtained:

(1) At time 1, the input APPs are P₀(\) , Pj(l). Label '0/0' indicates that the encoder output is '0' when its input is '0' while '1/1 ' indicates that the encoder output (codeword) is Ί ' when the input is also Ί '.

Referring to branch 510 in the trellis diagram 500 in Fig. 5, if the input is 0, the encoder

240 remains in state S₀(0) = So(l) = 00. Accordingly, the probability of the encoder being in state S₀(l) is given by the APP _°₀(1) :

P(So(l))=Po(l)

Similarly, a state transition from So(0) = 00 at time 0 to S₂(l) = 10 at time 1 occurs with the probability of one if the input is T. Accordingly, the probability of the encoder being in S₂(l) is represented by (see branch 512 in Fig. 5):

P(S₂(1))=P_!(1).

In this example, a transition from S₀(0) = 00 to Si(l) = 01 or S₃(l) = 1 1 is impossible because the values of the shift registers 245 and 245 are both zero at time 0. As such, their probabilities are:

PiS^l^O and PiSjO))^. According to equation (6), the output of the encoder 240 at time 1 is therefore:

X(l) = P(So(l))(l) + P(S₂(l))(-l) = Ροί - Ρ,Ο) = ,_(!) .

(2) At time 2, the input APPs are P₀(2) , ^ (2) . Referring to branch 520-510 in Fig. 5, the probability of the encoder remaining in state 00 is as follows:

P(So(2))=Po(2)Po(l),

which depends on P₀(\) , the APP that the input is 0 at time 1 , and P_Q(2) , the APP of receiving another 0 at time 2. Using a similar approach, the following can be obtained:

P(S,(2))=Po(2)P,(l) - according to branch 524-512;

P(S2(2))=P,(2)Po(l) - according to branch 522-510;

P(S₃(2))=P,(2)Pi(l) - according to branch 526-512.

According to equation (6), the output of the encoder 240 at time 2 is therefore:

X(2) = Po(2)Po(l)+P,(2)P₁(l)-P₁(2)Po(l )-Po(2)P₁(l)

= (P₀(2)-P₁(2))(Po(l)-P₁(l))

= X_ln (2) X_m (l) .

(3) At time 3, the input APPs are P₀(3) , J»(3) . According to branches 530-520-510 and 534-524-512 in Fig. 5, the probability of remaining in state 00 is depends the APP of b(k) =0 for k = 1 , 2, 3 as follows (see):

P(So(3)) = Po(3)P(S₀(2)) + P₀(3)P(S,(2))

= Po(3)Po(2)Po(l) + Po(3)Po(2)P,(l)

= Po(3)Po(2),

since P₀(l) + Pi(l) = 1. According to branches 538-522-510 and 542-526-512 in Fig. 5, P(S,(3))= P,(3)P,(2)Po(l) + P₀(3)P₁(2)P,(1) = P₀(3)P,(2).

According to branches 532-520-510 and 536-524-512,

P(S₂(3))= P₁(3)P₁(2)P₀(1) + Po(3)P₁(2)P,(l) = P,(3)P₀(2);

Similarly, according to branches 540-522-510 and 544-526-512,

P(S₃(3))= P,(3)P,(2)Po(l) + P,(3)P₁(2)P,(1) = P,(3)P,(2)

According to equation (6), the output of the encoder 240 at time 3 is therefore:

X(3) = P₀(3)Po(2)Po(l) + P₁(3)P₀(2)P,(1) + P₁(3)P,(2)P₀(1) + P₀(3)P,(2)P,(1) - Pj(3)Po(2)P₀(l) - P₀(3)Po(2)P,(l) - P₀(3)P,(2)P₀(1) - Ρ,(3)Ρ,(2)Ρ,(1) = (Po(3) - P,(3» (Po(2) - P,(2)) (P₀(l) - P,(l))

= X_in {3) X (2) X_in {\) where X_ln(k) = P^fy-P^k) is the input soft symbol estimate calculated from the input analog signals Y_r .

(4) Similarly, at time k, k >3, the input APPs are _°₀ the corresponding probabilities and output X(k) are:

P(So(*))=P₀(*)Po(*-l);

P(S,(*))=Po(*)Pi(*-l);

P(S₂(*))=P,(*)Po(*-l);

PiSaW^WP^-l);

X(k)= X_ln(k)X_ln(k-\)X (k-2)

Let L_x (k) = In X(k) and L_in(k) = In X _ln(k) , where for a complex number x = re^je, In x = In I r \ +j0. Therefore, for a negative real number *<0, In x = In | x \ +J . Denote by L_w =(L_ln(]),---,L_in(N)) and L_x =(L_x(\),---,L_x(N)),the following can be obtained:

L_x(k) = L k) + L_in(k-\) + L,„(k-2)=g_k (L_m)^T (7) md _x = G{L_IN)^T, (8) where g_k is the k-t row of G.

Equations (7) and (8) are derived for an exemplary constituent convolutional code (CC), but they can be applied to any channel code, which can be described by a generator matrix G, as shown in the following theorem.

Theorem 1: Let X,_n(k) represent the input soft symbol estimate (SSE) of the encoder 240, L_in{k) = \nX_in{k) and L_IN = {L_in(\),L 2),-,L_iM(N)) . Then given a generator matrix G of a linear constituent code G = (g,,g_{2 ,}---,g_N) , where g^T _k is the k-t row of G and y-th element of G is denoted by g_iJt e {0,1} , the logarithm of the SISO encoder outputs, for the soft inputs L_w , can be calculated as

L,= G(L_w)^r. (9)

The corresponding soft encoder outputs are given by

^) = exp(L^(*)) = exp(g_t(L_/JV)^r). (10)

To prove this Theorem 1, the following theorem is first proven. Theorem 2: Let U_l ={g_t} = l,y' = 0,...,N} be the set of non-zero coefficients in g, - (ga>8a>" >8iN) ^ = 0,...,N ^_{et c}^ ^ _tne ,·.^ _out _Ut _svmbol of binary encoder generated by G for source binary sequence B = (b(\),---,b(N)) . It is given by

c(0 = g,B^r =∑£,»*>(*)

(11) where the summation is over Galois Field 2 GF(2).

Let l(k) be the log likelihood ratio (LLR) value of b(k). Then the LLR value of c(i), denoted by /(c()), can be calculated as follows:

e²'-\

where tanh(*) =

e^2x + l^'

The above theorem can be directly proved by using the following equation [19]

l+nl^tanh('(*_?)/2)

/(.>(£,)0 b(k₂ )---( b(k„))=lnL(b(k_l)( b(k₂)---( b(k_n))=\n

Equation (10) can therefore be expressed as:

X (*) = _β ^χρ(ΐ, (*)) = exp(g_t (L_w)^r ) = exp ∑g_b In X f) = Π^βχρίΐ^η (¼,())* )

=Π(^ω = Π^« (14)

(=1

where U_k = {g_k)≠ 0, j = 1, · · · , N} is the set of non-zero coefficients in , g_kl e {0, 1} .

Theorem 1 formulates a simple SISO encoder structure that is shown in Fig.4, which can be implemented by using a conventional channel encoder that comprises shift registers 245 and 246 and modulo adders 243 and 244, as well as a logarithm computational module 242 and a exponential computational module 248 at the front and back of the conventional encoder.

Soft Symbol Estimate iSSE) A statistical model for the SSE is derived as follows and used for analyzing the performance of the DISC scheme. Referring to [6, 8, 21], the SSE X_in(k) can represented by the following model:

^ *) = ^ *)(l -« *)) = ^_nW(l -^) + ^W = a^_nW + ^W , (15) where X_in(k) is the exact transmitted symbol, n_jn{k) = -X_in{k){n_in{k) - ¼(£)) is the noise term in the SSE with a zero mean and variance of a_n , n_in {k) > 0 is an equivalent noise independent of X,„{k) with a mean μ_Λ ) and variance of

and - \ - μ_η.. It can be verified that X,„(k) and n_in{k) are independent. By substituting equation 15) into (14 X(k) can be represented as:

For simplicity, we consider a non-recursive convolutional code (NRCC) as the constituent code in the SISO encoder. Let denote by \ U_k \ the number of elements in

U_k . For the NRCC, | U_k |= A:₀ , which will be referred to as the row degree of G or the generator sequence weight (GS W) of g^PS. The GS W is also defined as the number of

PS

ones in its generator sequence of g .

Denote by C the encoder output of the source binary sequence B, based on the generator matrix G, and let X_g = (X_g (l), X_g (2), · · ·, X_g (N)) represent the modulated sequence of C. Then, X(k) can be represented as:

where a_Q = a^K° , X_g (k) = ]~[ X_in(j) is actually the modulated k-th encoder output symbol of B, n_ml(k) is the equivalent noise of the soft encoder with a zero mean and variance of

The structure of the SISO encoder 240 described above is obtained when the inputs to the encoder are the soft symbol estimates. It should be understood that the above SISO encoder structure 240 is applicable to any analog input signals carrying the source symbol information. That is, given analog input signals X_ln(k) , k=l ,... fl, the corresponding &-th SISO encoder output signal X(k) can be calculated as: (*) = expfc. (L_w)^r)= expf∑ , ln _m( ) = JJXM)

(19)

Although the encoding process has been described using the exemplary encoder 240 in Fig. 4, it should be noted that other encoder structures can also be used. The soft symbol estimate is the optimal input to the SISO encoder 240 in terms of maximizing the SISO encoder output SNR in one or more embodiments.

Theorem 3: Given an input analog signal carrying the source information symbol, the soft symbol estimate is the optimal input to the soft encoder in terms of maximizing the SNR of the SISO encoder output.

Referring to step 340 in Fig. 3 again, the corresponding soft encoder output at the p-†h relay node 200 at time k is expressed as:

X_p(k) = _a;^>X_g k) + n_{0Ul p}{k) , (20) where a_p = \ - μ_{Λ ρ} , μ_{Λ ρ} is the mean of equivalent noise n_ln (k) in the SSE as shown in equation (15), X_gtP(k) is the modulated fc-th exact encoder output symbol of source binary sequence B, based on the generator matrix G_p and n_{ml p}{k) is the soft encoder equivalent noise with a zero mean and variance of

σ^{,η ρ} is the variance of the equivalent noise in the soft input to the SISO encoder of relay node p.

Assuming that all relay nodes 200 use the same transmission power of P_T, the signals transmitted from relay node p can then be written as:

X_{r p}(k) = fi_pX_p(k) ^ ₍₂₂₎ where β_ρ is a normalization factor calculated from the transmitted power constraint at relay node p, given by

At the destination node 120, the received signal from the -th relay node 200 is:

= h_{rd p}a;^K X_g__p{k) ₊ n_d ^k)

where h_{d p}(k) = h_{rd p}fi_pn_{ml p}(k) + n_{d p}(k) is an equivalent noise with a zero mean and variance of: In the above equation,

E(n_nuU(k)n_OUIJ(k))= 0

Performance Analysis

The SISO encoding at the relay nodes 200 can bring the system some coding gains, but on the other hand equations (17-18) show that the encoding of noisy SSE will enhance the noise power at the destination node 120. Thus it is not clear whether the coding gain can surpass the noise enhancement in the DISC and whether such encoding can bring any overall gain. A quantitative analysis of the DISC scheme performance is presented below.

By substituting equation (23) into (25), the variance of the equivalent noise at the destination node 120 in equation (25) can be expanded as

where ^{7 sr} -^{p p in p} is the input SNR of the SISO encoder at the /?-th relay.

From equations (24) and (26), the instantaneous destination SNR, corresponding to the signals generated by the p-t constituent encoder, is represented as follows:

1 (27) a² + P \h . J² 1 - (ι + " >ν„.,Γ'

hrd.p l I ^σ1 is ^tne instantaneous SNR in the link from relay p to the destination and the last equation is a high SNR approximation.

Since calculating the exact BER is extremely complicated, an asymptotic performance at high SNR is considered to provide some insights into the system design. Assuming that "^d-p ^ can be approximated as a Gaussian random variable, then the DISC BER can be approximated at high SNR as:

where d_{min p} is the minimum Hamming weight (MHW) of a nonzero codeword, which is also equal to the code minimum Hamming distance (MHD), generated by the constituent encoder 240 at the p-\ relay node 200.

Let d_min denote the MHW of a nonzero codeword generated by all K constituent encoders. d_mjn and d_{min p} can be obtained either by simulations or by deriving its bounds. Theorem 4 presents a simple bound for d_min and i/_mi .

Theorem 4: Consider a non-recursive convolutional code C, generated by K constituent codes with respective generator sequences gf^s , g ^s , g£^s . Let d_{min p} represent the MHD of the codes generated by the p-Xh constituent code with generator sequence g^p _p , d_min represent the MHD of the overall codeword generated by K constituent codes, and let ^p be the Hamming weight of a codeword generated by the p-th encoder for the input sequence of (1 0 0 0...0). Then the following simple bound can be derived for d„ mm- and d m\-n,p„ , ' d < w K ^^{min ≤}∑ ^{K p}

m^m-" - ^■·" = * and , (29) where κ_ρ is row degree of the generator matrix for the p-Xb. constituent code, which is equal to the number of Is in its generator sequence " . We refer to κ_ρ as the generator sequence weight (GSW) of g^FS .

Table 1 shows the exact MHDs and the MHD bounds calculated in (29) for rate 1/2, 1/3 and 1/4 codes with various memory lengths. The codes are obtained from [20]. It is shown that the difference between the bound in equation (29) and the exact MHD is at most 1 for the codes listed in the table and for most of the codes the bound is equal to the exact MHD.

Table 1: Comparison of Exact MHD and MHD Bound in equation (29) for

Rate 1/2, 1/3 and 1/4 codes

Using the MHD bound in Theorem 4, the BER in equation (28) can be further approximated as follows:

(30) where

From equations (30)-(31), P_b and ρ_ρ {κ_ρ,γ_τα,γ^ _ίη ^ are a monotonic decreasing and increasing function of κ_ρ , respectively. To decrease the error rate P_b , one should make the GSW κ_ρ as large as possible by increasing its memory length, as with the conventional convolutional codes. However, κ_ρ , ρ=\ ,..., K cannot be chosen arbitrarily as the code may become catastrophic for certain combinations of GSW values. The code construction has to be non-catastrophic, which means that the codes generated are observable. Some examples of good non-catastrophic codes are shown in Table 1 for various code rates. From the table, GSWs are different for different p for most of good codes.

Allocation of Constituent Codes

Referring now to the flowchart 600 in Fig. 6, a method for allocating K constituent convolutional codes with respective generator sequences gf^s , g£⁵ , g£^s to K relay nodes 200 in the relay network 100 is explained.

In this example, the allocation of codes is performed by the destination node 120, but it should be understood that the allocation may also be performed by the source node 1 10 or by one of the relay nodes 200.

As shown in step 610, the input SNR of the SISO encoder 240 at the p-X relay node 20 , y_sr_i„_iP , is determined for each of the relay nodes p = Ι,. , .,Κ in the network 100. The input SNR γ„ _ρ is directly calculated from the soft symbol estimate of the decoder at each relay node 200. To determine which constituent code should be assigned to which relay node p, the input SNRs y_{sr n J} are then ordered in a decreasing order; see step 620. The reordered

SNR values are represented as (γ„,_Μ) , r_{srJn 2)} , · ··, γ_!Γ ._{Κ) ) _> ^where

Ysr,in.m — " '— Y srjn,(K ) 2)

Then in steps 630 and 640, the GSWs (κ_ι ,κ₂,...,κ_κ ) of the available constituent codes with generator sequences g ^s , g£^s are then calculated or retrieved from a data store, and ordered in a decreasing order to obtain re-ordered GSWs:

K_{0 )}≥K_m≥~ .≥K_(Ky (33)

Theorem 5: Consider a parallel relay network consisting of K relay nodes 200. In the DISC, each relay performs a SISO encoding, where the relay constituent codes can be the existing good convolutional or other linear codes. Assume that a good convolutional code generated by K constituent convolutional codes with generator sequences g ^s , g^ , g^p _K ^s has already been found. Let us denote by κ_ρ the GSW of

%_p ^s . Then the optimal code construction is to assign the code with the -th largest

GSW ^KW to the relay node 200 with the p-\ largest input SNR γ„ _Αρ)■ In this way, the system achieves the optimal BER performance for given constituent codes with generator sequences g ^s , g£^s g^P _K ^s .

According to Theorem 5 below, the code with the p-t largest GSW κ_(ρ) is allocated to the relay node 200 largest input SNR Y„^_p) ; see step 650. Since the GSW values are matched to the corresponding input SNRs and the constituent code with a large GSW value is assigned to the relay node 200 with a large SNR, the allocation minimises the p

BER * for the given GSWs ( κ₍₁₎ , κ₍₂₎ ,..., κ_{Κ) ). The allocation of codes is then broadcasted to all relay nodes 200 in the network 100; see step 660.

Let _{sr p} and γ_{ν ρ} = y_{sr p} \ h_{sr p} \² be the average and instantaneous SNR in the link from the source to the p-ih relay node 200. Then, using the fact that γ„ _Μ is monotonically increasing function of ^"·^ρ , two corollaries for AWGN and slow fading channels are set out as follows. Corollary 1: DISC Design for AWGN Channels: The optimal code construction of DISC for AWGN channels is to assign the code with the p-th largest GSW κ_{ρ) to the relay node with the p-th largest average SNR _ir . Corollary 2: DISC Design for Slow Fading Channels: The optimal code construction of DISC for fading channels is to assign the code with the p-th largest GSW κ_(ρ) to the relay node with the p-th largest instantaneous SNR γ„_ρ . Therefore, at different time slots, different codes may be allocated to different relays. The destination needs to broadcast to all relays the ordering of instantaneous SNRs y_{sr p} of K relays. Each relay then selects the code based its ordering.

To show the gain of the DISC with the optimal pairing over a DISC with un-ordered pairing and the soft information relaying (SIR), consider a simple example encoder with a rate ½ convolutional code of memory length of 3. The generator sequences of two constituent codes are gf^s =(101) with K_m = 2 and g£^s =(l 1 1 ) with t ₍₂₎ = 3 .

Consider an AWGN channel and assume that the average input SNR of relay 1 is larger than that of relay 2. Then we have y_{sr t} > Υ_5τίηΛ · Then according to Corollary 1 the optimal pairing strategy is to assign the constituent code g(l) = g£^s =0 H) with the maximum GSW to relay 1 with the maximum SNR γ„ and g(2) = ⁵ =(101) with the minimum GSW to relay 2 with the minimum SNR γ„^_Λ ·

To show the performance gain of the proposed scheme, assume that

>

Then for an un-ordered pairing, assume that g(l) and g(2) are assigned to relays 1 and 2, respectively, *Ί ^{= 2} and ^{K = 3} and

For the optimal pairing, the following are obtained:

11 5 3^ + 2(1 + a.) opi ∑ 'o/».p('^f(p .i i.(p) ' ?''i' )^— ^■ + -

P-l

Similarly, for the conventional soft information relaying scheme,

get

Then we have

o_p/ ~ ^ p_opl - PAP are the coding gains of the DISC with the optimal code pairing over the DISC with an un-ordered pairing and the conventional SIR scheme, respectively. From equations (34-35), we can see that the DISC with the optimal pairing always outperforms the DISC with an un-ordered pairing and the conventional SIR scheme at high SNR.

Simulation Results

All simulations are performed for an exemplary system using the BPSK modulation and a frame size of 130 symbols over AWGN and quasi-static fading channels will now be analysed. In this example, it is assumed that all relay nodes 200 use the code with the same number of states. Thus if there are K relays, the convolutional code with rate \IK can be used in K relays, and each relay uses one constituent code. For example, for the relay network with 2, 3 and 4 relays, the convolutional codes with rates 1/2, 1/3 and 1/4 listed in Table 1 can be used as constituent codes at the relay nodes 200.

Fig. 7(a) and Fig. 7(b) compare the frame error rate (FER) performance in a network with 2 relay nodes 200 of soft information relaying (SIR), DISC with optimum and un- ordered code pairing, as well as the conventional decode and forward (DAF) for various numbers of states over AWGN channels for γ„ = y_rd , γ„ = +3dB, respectively. The average SNR in the link from the source node 110 to the 1st relay node 200 is y_{sr i} = y_sr and the average SNT in the link from the source node 110 to the 2nd relay node 200 is _{sr 2} = f_sr + 3dB . Here the optimal and un-ordered assignment is the same as the assignment according to Corollary 1. It has been shown in [6, 24] that the SIR always outperforms the AAF, so the SIR scheme is only used as a reference.

From Fig. 7(a) and Fig. 7(b), the performance of the DAF gets worse as the number of relay encoder states increases. Such performance degradation is due to the error propagations in the DAF scheme. In the DAF scheme, when decoding errors occur at the relays, the process of decoding and re-encoding causes errors to propagate into subsequent symbols. The longer the encoder memory, the larger the number of subsequent symbols affected by the decoding errors. Therefore, the error rate of the DAF will increase with the number of states. For example, Fig. 7(b) shows that the FER performance of the DAF for the 4-state and 8-state codes is worse by 0.5dB and 0.7dB, respectively, than for the 2-state code at the FER of 10^"3.

However, the SISO encoder using the DISC scheme can effectively mitigate the error propagation in the re-encoding process and at the same time provide a significant distributed coding gain. Therefore, the DISC provides significant coding gains compared to the SIR without relay re-encoding and the gain increases as the number of states increases at high SNR. For example, as shown in Fig. 7(b), the DISCs with 2, 4 and 8-state are superior to the SIR by about 1.4dB, 1.8dB and 2dB, respectively.

This result is consistent with the analysis discussed above, showing that the DISC performance improves as the number of states at the relay encoder increases. Furthermore, from Fig. 7(a) and Fig. 7(b), the DISC with optimal code pairing also brings significant gains compared to the DISC with the un-ordered pairing. For example, as shown in Fig. 6(b), the 4-state code with the optimal code pairing is superior to that with the un-ordered pairing by 2dB at the FER of 10^'3. This validates the effectiveness of the proposed design criteria.

Fig. 8(a) and Fig. 8(b) compare the performance over fading channels for a network with 2 relays for γ„ = f_rd , f„ = f_rd +10dB, respectively. We set γ„_λ = y_{sr 2} = y_sr . It can be observed from Fig. 7(a) and Fig. 7(b) that the DISC and SIR can achieve the full diversity order of 2, but the conventional DAF can only achieve the diversity order of 1 due to error propagation. The DISC substantially outperforms the SIR scheme over fading channels too. For example, the DISC with 2, 4 and 8 states can bring about 2dB, 2.5dB and 3dB gains, respectively, relative to the SIR scheme, for y_sr = f_rd and the gains are increased to 2.5dB, 5dB and 5.5dB, respectively, for γ„ = f_rd +10dB. That is, the coding gain brought by the DISC increases when the source-relay link quality is improved. It can also be observed that the coding gain increases as the number of relay encoder states increases, which is contrary to the conventional DAF scheme where the performance degrades as the number of encode states increases. Furthermore, the DISCs with optimal pairing are always superior to the DISCs with un-ordered pairing, but the differences are not as large as on AWGN channels, especially as the number of encoder state increases.

Fig. 9(a) and Fig. 9(b) show the results for three relay nodes 200 over AWGN channels, and Fig. 10(a) and Fig. 10(b) show the results for fading channels. From these figures, trends similar to that for the case with two relays are observed. That is, the DISC can bring significant gains over the SIR and DAF on both AWGN and fading channels and the gains increase as the number of state increases. For the fading channels, both DISC and SIR schemes can achieve the full diversity order of 3 while the DAF can only achieve the diversity order of 1 due to error propagation. Also the DISCs with optimal pairing always outperform the DISCs with the un-ordered pairing for various numbers of states. Furthermore, the coding gain of DISC over SIR slightly increases as the number of relay increases from 2 to 3. From the above results, we can see that the re-encoding in the conventional DAF schemes cause serious error propagation and thus does not provide any coding advantages. By contrary, the proposed DISC can effectively mitigate the error propagation in the re-encoding and provide significant distributed coding gains, thus substantially outperforming the soft information relaying (SIR) and conventional DAF schemes.

Proofs

(i) Proof of Theorem 1

Let X_in {k) and l(k) represent the SSE of source symbol s(k) and LLR of source bit b(k). Then they have the following relationship,

By substituting equation (13b) into (12), we have

By using equation (13b) again, the SSE of c(i) , denoted by X(k) , can be calculated as

⁼ FU = e p(*(L_w)^r) · (40)

This proves Theorem 1.

(ii) Proof of Theorem 3

From equations ( 17) and ( 18), the output SNR of SISO encoder is given by

al 1 1

(ΐ + σ>/α²)'°-1 (l + ri r-l

where From (19a), it can be observed that in order to maximize ^SR-°'" , needs to be maximized. It has been proved in [6] that the SSE is the SNR maximizing estimate of the source symbols. Thus, the SSE is the optimal input to the SISO encoder in terms of maximizing the SNR of SISO encoder output. This proves Theorem 3.

(iii) Proof of Theorem 5 Lemma 1; Given the positive real numbers x_x >x >0 and y_} > y₂ >0, the following relationship always holds,

1 1 1 1

x +y_} x₂+y₂ x_}+y₂ x₂+y_x

The proof of the above result is straightforward and is omitted here. Now let us use the

Lemma to prove Theorem 5. Let's rewrite as follows P,( .r_w)^{s YrdY} =r- -1 ⁽⁴²⁾ where C₀ = γ_Μ, x_p = \/κ_ρ, and y_p = C₀ ly_srinp .

Let x₍₂₎, ···, x_{K) and y_m, y_{2), ···, y_{K) represent the re-ordered values of x x₂, ···, x_K and y₂, ···, y_K . Then from equations (32) and (33), we have ½ ^{≤ χ}(2) ···^{≤ χ}(κ) and y_m≤ y_m ···≤ '«)· (⁴³> Now let us determine how to distribute {Χ₍₁₎,···,Χ _Κ)} and {y^₎,---,y_{K)} to form K pairs [x_p,y_p), p=\ an only be assigned to one and only one pair, so as to As can be seen from equation (42), this is

equivalent to maximizing

^∑ _*=∑—— ^l =∑/( ,) (44)

P= p + y p p=\

where f(x_p , y_p ) = (x_p + y_p )^"' .

Assume that the optimal K pairs of (x_p,y_p) for p=\,...,K, are {x_m,y ), (Λ:₍₂₎,^ ),..., (^₍Λ:_)»^ )· Now we prove this theorem by contradiction. Assume that y_h , y , y_h do not exactly follow the relationship of y_Jt≤y_h---< y_h . Then there must exist at least two integers p, q, such that y_jf > y for p<q. Since x_{q)≥ x_(p) and y_jf > y^ , then

Variations

It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

For example, although the example has been described using a time division multiplexing scheme, it will be appreciated that frequency division multiplexing may be used. It should also be understood that, unless specifically stated otherwise as apparent from the following discussion, it is appreciated that throughout the description, discussions utilizing terms such as "receiving", "processing", "retrieving", "selecting", "calculating", "determining", "displaying" or the like, refer to the action and processes of a computer, or similar electronic processing unit, that processes and transforms data represented as physical (electronic) quantities within the processing unit's registers and memories into other data similarly represented as physical quantities within the memories or registers or other such information storage, transmission or display devices.

It should also be understood that the methods and systems described might be implemented on many different types of processing devices by computer program or program code comprising program instructions that are executable by one or more processors. The computer program instructions may include source code, object code, machine code or any other stored data that is operable to cause a processing system to perform the methods described. The computer program can be written in any form of programming language, including compiled or interpreted languages and can be deployed in any form, including as a stand-alone program or as a module, component, subroutine or other unit suitable for use in a computing environment. The computer program can be executed on one computer or on a multiple computers at one site or distributed across multiple sites and interconnected by a communication network.

It should also be understood that the methods and systems may be provided on any suitable computer readable media. Suitable computer readable media may include volatile (e.g. RAM) and/or non-volatile (e.g. ROM, disk) memory, carrier waves and transmission media (e.g. copper wire, coaxial cable, fibre optic media). Exemplary carrier waves may take the form of electrical, electromagnetic or optical signals conveying digital data steams along a local network or a publically accessible network such as the Internet. Computer components, processing units, engines, software modules, functions and/or data structures described herein may be connected directly or indirectly to each other in order to allow any data flow required for their operations. It is also noted that software instructions or module can be implemented using various of methods. The software components and/or functionality may be located on a single device or distributed over multiple devices depending on the application. Reference in the specification to "one embodiment" or "an embodiment" of the present invention means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrase "in one embodiment" appearing in various places throughout the specification are not necessarily all referring to the same embodiment. Unless the context clearly requires otherwise, words using singular or plural number also include the plural or singular number respectively.

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Claims

Claims:

1. A method for relaying signals in a wireless network comprising a source node, a destination node and one or more of the relay nodes, the method being performed at a relay node and comprising:

(c) transmitting the soft-encoded signal to the destination node.

2. The method of claim 1, wherein the soft input comprises a sequence of soft symbol estimates of information symbols received from the source node, each soft symbol estimate being a posteriori probability (APP) of the corresponding information symbol given the signals received from the source node.

3. The method of claim 2, wherein the soft-encoded signal comprises a sequence of codewords that are each encoded by the soft-input-soft-output encoder as a product of one or more of the soft symbol estimates of the soft input.

4. The method of any one of the preceding claims, wherein the soft-input-soft- output encoder further comprises a logarithm computational module, and a exponential computational module, and step (b) further comprises:

(i) calculating a logarithm of the soft input;

(ii) encoding the logarithm of the soft input using the linear encoder based on the generator sequence of the constituent code; and

(iii) calculating an exponential of the encoded soft input to obtain the soft- encoded outputs.

5. The method of claim 4, wherein the soft-input-soft-output encoder uses one of the following linear codes: convolutional coding, block coding, low density generator matrix (LDGM) coding and low density parity check code (LDPC) coding.

6. The method of any one of the preceding claims, wherein step (c) further comprises soft decoding the signals received from the source node before step (a) if the received signals are encoded.

7. The method of any one of the preceding claims, wherein at the destination node, the soft-encoded signals from multiple relay nodes are used to form a codeword and decoded to estimate information symbols sent by the source node.

8. The method of any one of the preceding claims, wherein the constituent code is allocated based on an input signal-to-noise-ratio (SNR) value of the soft-input-soft- output encoder and a weight of the generator sequence of the constituent code.

9. A method of processing signals at a destination node in a wireless network comprising a source node, a destination node and one or more relay nodes, the method comprising:

(a) receiving soft-encoded signals relayed by one or more of the relay nodes according to the method of any one of claims 1 to 8;

10. A wireless relay system comprising:

(a) a source node operable to broadcast signals;

(b) one of more relay nodes operable to:

1 1. A method for allocating constituent codes to relay nodes in a wireless network comprising a source node, a destination node and the relay nodes, the method comprising:

(a) determining a weight of a generator sequence of each of the constituent codes;

(c) allocating one of the constituent codes to one of the relay nodes based on the weight of the generator sequence of the constituent code and the SNR value of the relay node, wherein the allocated constituent code is used for soft encoding of signals received at the relay node.

12. The method of claim 1 1 , wherein in step (c), the constituent code with generator sequence having the largest weight is allocated to the relay node with the largest SNR value, the constituent code with generator sequence having the second largest weight is allocated to the relay node with the second largest SNR value, and so on.

13. The method of claim 11 or 12, further comprising ordering the input SNR values and the weights in a decreasing order before step (c), and allocating the constituent codes in step (c) based on the ordered weights and input SNR values.

14. The method of any one of claims 1 1 to 13, where the SNR values are average SNR values if a wireless channel between the source node and the relay node is an Additive White Gaussian Noise (AWGN) channel.

15. The method of any one of claims 1 1 to 14, where the SNR values are instantaneous SNR values if a wireless channel between the source node and the relay node is a slow fading channel.

16. The method of any one of claims 1 1 to 15, further comprising repeating steps (a) to (c) at different time slots.

17. The method of any one of claims 11 to 16,

wherein the relay node encodes a soft input to a soft-input-soft-output encoder based on a generator sequence of the allocated constituent code; and wherein the soft input is determined at the relay node based on signals received from the source node, and the soft-input-soft-output encoder comprises a linear encoder.

18. A mobile communications equipment operable to perform the method according to any one of claims 1 to 9 and 11 to 17.

19. Computer program comprising executable instructions operable to cause a mobile communications equipment to perform the method according to any one of claims 1 to 9 and 1 1 to 17.