WO2018133939A1

WO2018133939A1 - Apparatus and methods for probability shaping operations

Info

Publication number: WO2018133939A1
Application number: PCT/EP2017/051070
Authority: WO
Inventors: Onurcan ISCAN; Wen Xu
Original assignee: Huawei Technologies Duesseldorf Gmbh
Priority date: 2017-01-19
Filing date: 2017-01-19
Publication date: 2018-07-26
Also published as: CN110199490A; CN110199490B

Abstract

A controller comprises an input configured to receive data that defines a length of a message to be transmitted, k, and a number of channel units, N_RE, available for transmitting that message. The controller also comprises a parameter generator configured to determine, in dependence on k and N_RE, one or more parameters for controlling an operation. The operation prepares the message for transmission by transforming an original signal with a first probability distribution into a transformed signal with a second probability distribution. The controller is thus able to determine the parameters that are required for controlling a distribution matching operation, or other operations related to the PSCM system.

Description

Apparatus and Methods for Probability Shaping Operations

This invention relates to apparatus and methods that assist with shaping the probability of signals to improve transmission performance.

Probabilistically Shaped Coded Modulation (PSCM) is a new transmission scheme which can support bandwidth efficient transmission with near Shannon capacity performance. PSCM offers significant performance improvements, especially at high spectral efficiencies (SE), where coded modulation schemes with uniformly distributed channel input symbols (such as BICM in LTE) are suboptimal for many channels (e.g. AWGN channels). The performance improvement of PSCM mainly comes from the smaller shaping loss compared to the conventional schemes.

Transmitter and receiver chains in communication systems usually include a number of different blocks for performing specific tasks. These include multiplexers, demultiplexers, channel encoders, decoders, interleavers, deinterleavers, etc. In general, each block has to be provided with at least one parameter that defines how its task is performed. In some communication systems, the relevant parameters can be fixed so they can be set once (e.g. to agreed default values) and then left. In other communication systems, transmitter and receiver chains should be capable of changing the parameters dynamically in accordance with some predefined criteria. Often the parameter selection for one block influences the parameter choice of other blocks. PCSM transmitter and receiver chains include extra blocks - such as a shaping encoder (ShEnc) at the transmitter side and a shaping decoder (ShDec) at the receiver side. A probability distribution matcher (DM) can be considered as a special form of shaping encoder and may be implemented using, e.g. an arithmetic or Huffman coding/decoding algorithm. All these blocks to be considered when determining parameters. Parameter selection cannot be adopted directly from existing coded modulation systems. Currently, there is no systematic technique for determining the parameters for PCSM transmitter and receiver chains.

The PCSM scheme typically consists of a shaping encoder (ShEnc) or probability distribution matcher (DM) and a channel encoder (ChEnc) at the transmitter side, and a channel decoder (ChDec) followed by a shaping decoder (ShDec) or probability distribution dematcher (DM^-1) at the receiver side. The following description uses the terms shaping encoder and distribution matcher and the terms shaping decoder and distribution dematcher interchangeably and does not make any distinction between them (unless otherwise stated). The PSCM brings two different advantages. First, the DM transforms uniformly distributed bits of the input message to a non-uniform distribution. The channel input symbols are therefore distributed according to a target probability distribution that achieves (or approaches) channel capacity. Second, by changing the parameters of the DM, the transmitter can adjust the rate of the transmission without having to change the parameters of the Forward Error Correction (FEC) code. These two aspects are different from conventional coded modulation schemes (such as Bit-Interleaved Coded Modulation (BICM)), where there is no distribution matching to optimise the distribution of the channel input symbols, and where rate matching is achieved by adjusting the parameters of the FEC code. One drawback of a PSCM system is its inflexibility in terms of code word length. In PCSM, the transmission rate is adjusted by changing the input message size; the code word length stays constant. However, some DMs are only configured to accept messages having one of a predetermined set of sizes. An example is the popular 'Constant Composition Distribution Matcher' (CCDM), which offers excellent distribution matching performance but a finite set of possible input lengths, depending on the output length and the target distribution. This property can be advantageous for many applications, particularly where the number of resource elements per unit of transmit data is fixed, but more flexibility in terms of code word length may be beneficial for some other applications.

It is an object of the invention to provide concepts for improving the operation of devices that are configured to shape the probability distributions of signals.

The foregoing and other objects are achieved by the features of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures.

According to a first aspect, a controller is provided that comprises an input configured to receive data that defines a length of a message to be transmitted, k, and a number of channel units, NRE, available for transmitting that message. The controller also comprises a parameter generator configured to determine, in dependence on k and NRE, one or more parameters for controlling an operation. The operation prepares the message for transmission by transforming an original signal with a first probability distribution into a transformed signal with a second probability distribution. The controller is thus able to determine the parameters that are required for controlling a distribution matching operation, or other operations related to the PSCM system.

The parameter generator may be configured to determine a parameter, in dependence on the data, which controls whether or not the message will be prepared for transmission by the operation. This enables the operation to be disabled in appropriate circumstances, which saves power.

The parameter generator may be configured to generate each of the one or more parameters using a deterministic function. This makes the operation predictable, since a given set of inputs will always produce the same control parameters.

The parameter generator may be configured to generate parameters that define one or more of: a spectral efficiency associated with the transmission of the message; a modulation order; a code word length; a length of an input to a distribution matcher; a length of an output generated by the distribution matcher; a part of the message that is not to be input into the distribution matcher; a rate of an error correcting code; a length of one or more outputs generated by a demultiplexer; and a number of filler bits. Each of these define an important aspect of the distribution matching operation.

According to a second aspect, a method is provided that comprises receiving data that defines a length of a message to be transmitted, k, and a number of channel units, NRE, available for transmitting that message. The method also comprises determining, in dependence on k and NRE, one or more parameters for controlling an operation. The operation prepares the message for transmission by transforming an original signal with a first probability distribution into a transformed signal with a second probability distribution. According to a third aspect, a padding unit is provided that is configured to receive a message that is to be transmitted. It also introduces a number of bits into that message. The padding unit also outputs the message and its introduced bits for processing by an operation that will prepare the message for transmission. The operation will transform an original signal with a first probability distribution into a transformed signal with a second probability distribution. Introducing extra bits into the message increases flexibility and can lead to performance improvements.

The number of bits may be selected in dependence on an input message length associated with a distribution matcher that is configured to perform the operation. This enables the length of the input message to be freely chosen while still meeting any input length requirements imposed by the distribution matcher.

The number of bits may be selected in dependence on a desired rate of transmission of the message and/or in dependence on one or more parameters of a distribution matcher that is configured to perform the operation. This enables the input message to meet a desired transmission rate while still matching the input requirements of the distribution matcher. The number of bits may be selected in dependence on a desired error detection and/or error correction performance. This enables the bits to contribute to improved transmission performance.

The padding unit may be configured to generate one or more of the number of bits in dependence on the message. This enables the additional bits to provide error detecting/correcting information to the receiver.

The padding unit may be configured to generate the one or more bits by applying a deterministic function to the message. This enables the additional bits to be reliably generated.

The padding unit may be configured to generate the one or more bits by encoding the message with an error detection and/or error correction algorithm. This leads to improved error detection/correction performance. According to a fourth aspect, a method is provided that comprises receiving a message that is to be transmitted. It comprises introducing a number of bits into that message. The message also comprises outputting the message and its introduced bits for processing by an operation. The operation, which transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution, will prepare the message for transmission.

According to a fifth aspect, a transmitter is provided that is configured to receive a message that is to be transmitted. The transmitter is configured to determine an efficiency associated with the transmission of the message. The transmitter is also configured to select either a first transmit scheme or a second transmit scheme for preparing the message for transmission, in dependence on the determined efficiency. The first transmit scheme includes an operation that transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution. The second transmit scheme does not include the operation that transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution. This enables the operation to be disabled in appropriate circumstances, which can save power.

The transmitter may be configured to select either the first transmit scheme or the second transmit scheme in dependence on a respective shaping gain that is expected to be achieved by each of the first and second transmit schemes at the determined efficiency. The transmitter thus assesses whether or not the first transmit scheme is expected to result in a performance benefit, which provides a sound basis for deciding whether or not that scheme should be implemented.

The present invention will now be described by way of example with reference to the accompanying drawings. In the drawings:

Figure 1 shows an example of a transmitter chain that incorporates a controller and a padding unit according to embodiments of the invention; Figure 2 shows an example of a controller according to an embodiment of the invention;

Figure 3 shows an example of a padding unit according to an embodiment of the invention;

Figure 4 shows an example of a method of operating the exemplary transmitter chain illustrated in Figure 1 ; and Figure 5 shows a further example of a controller according to an embodiment of the invention.

Figure 1 shows an example of a transmitter chain, which is shown generally at 101 . It is configured to implement a Probabilistically Shaped Coded Modulation (PCSM) transmission scheme. The transmitter chain includes a demultiplexer 102, a distribution matcher (DM) 102, a symbol-to-bit mapper 104 and a DM mapper 105. It also includes an encoder 106, a modulation interleaver 107 and a symbol mapper 108. Figure 1 also shows a controller 1 1 1 and padding unit 1 12. These blocks are optional and may be implemented individually with a transmitter chain or together.

An example of a controller is shown in Figure 2. The controller, shown generally at 200, comprises an input 201 . The input is configured to receive data that defines a length of a message to be transmitted. This length can be defined as "k". It also defines a number of channel units that are available for transmitting that message. The expression "channel units" denotes discrete resource elements (e.g. time-frequency resource elements in an OFDM-based LTE or 5G system) that the communication system can assign to the transmission of data. It encompasses, for example, assigned time slots, assigned frequencies, assigned codes (e.g. in the sense of code division multiplexing), and any combination thereof. The number of channel units can be defined as "N_RE".

The controller 200 also comprises a parameter generator 202. The parameter generator is configured to determine one or more parameters. These parameters are for controlling an operation that will prepare the message for transmission. The operation is associated with distribution matching. It operates to transform an original signal with a first probability distribution into a transformed signal with a second probability distribution.

Each of the signals that is processed by the transmitter chain shown in Figure 1 can be considered as representing a series of bits or symbols. Those bits or symbols are usually taken from an alphabet that defines the bits or symbols that are available to the message. For example, a binary alphabet is the set {0, 1 }. The "probability distribution" of a signal defines the relative proportions of the different alphabet members that the sequence contains. So, for example, the probability distribution of a binary sequence refers to its relative proportions of '1 's and O's. The distribution matching operation is configured to change the probability distribution of a signal, which can be referred to as "shaping".

In some implementations, the original signal that is received by the transmitter chain is a uniform sequence, i.e. a sequence in which the relative proportions of the alphabet members are the same. The distribution matching operation is preferably configured to transform these uniform distributions into "biased" distributions, where the term "biased" refers to the probability of the different alphabet members in a sequence being different.

The parameter generator generates the parameters for controlling the DM operation in dependence on k and NRE. Preferably this is done using a deterministic function, so that the parameter generator reliably generates the appropriate parameters for a given combination of k and NRE.

One of the parameters generated by the parameter generator may determine whether or not the message will actually be processed by the probability shaping operation at all prior to transmission. This means, for example, that the parameter generator can cause the DM in a PCSM transmitter chain to be switched off. The transmitter chain might then operate as a conventional Bit-Interleaved Coded Modulation (BICM) transmitter chain. The decision to switch off the DM may be taken if there is little expectation that distribution matching will provide any advantage, e.g. in scenarios where nearly no shaping gain is expected at the operating spectral efficiency (SE). This can be particularly helpful for power-constrained user equipment (UE).

An example of a padding unit is shown in Figure 3. The padding unit 300 comprises an input/output 301 that is configured to receive a message that is to be transmitted. The padding unit also comprises a bit generator 302 that is configured to introduce a number of bits into that message. The input/output is configured to output the message and its introduced bits so that the message can be prepared for transmission. This preparation involves the message being processed by an operation that transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution. The operation may be associated with distribution mapping.

The padding unit 300 at the input of a PSCM transmitter chain can be used to add a variable number of bits to the message. One reason for doing this might be to change the length of the message, so that it matches the specific length requirements of DM 103. The added bits may be any filler bits, such as a series of zeros or ones. In one example the padding unit includes an optional encoder 303. The encoder is configured to generate the one or more bits by encoding the message with a suitable error detection and/or error correction algorithm. This helps to improve error detection/correction performance. A DM can be viewed as a device that maps one sequence to another sequence via a one-to-one mapping. The DM 103 can therefore be used to implement an error detection scheme, since an error can be declared if no valid sequences are found during distribution dematching (DM^-1). However, error correction performance of DMs is mostly poor. Therefore, the encoder in the padding unit can be used to combine a DM with an additional error detection scheme (such as Cyclic Redundancy Check (CRC)) to improve the error detection performance.

The structures shown in Figures 1 to 3 (and all the block apparatus diagrams included herein) are intended to correspond to a number of functional blocks. This is for illustrative purposes only. Figures 1 to 3 are not intended to define a strict division between different parts of hardware on a chip or between different programs, procedures or functions in software. In some embodiments, some or all of the signal processing techniques described herein may be performed wholly or partly by a processor acting under software control. In some embodiments, some or all of the signal processing techniques described herein are likely to be performed wholly or partly in hardware. This particularly applies to techniques incorporating repetitive arithmetic operations, such as CRC calculations, appending bits, parameter calculation and mapping and shaping. In some implementations, the functional blocks are expected to be implemented as dedicated hardware in a transmitter chain.

The description below concentrates on the transmitter-side, since it is the transmitter- side that mandates the receiver-side processing. It should be understood, even where this is not explicitly stated, that the techniques described below as being performed on the transmitter-side will be mirrored on the receiver-side to reverse the transmitter- processing and obtain the original data sequence.

The specific components found in a transmitter/receiver chain are dependent on the exact waveform and telecommunications protocol that the transmitter/receiver is configured to implement. One or more implementations of the invention are described below with reference to an application in which the transmitter/receiver is configured to operate in accordance with a PCSM transmission scheme. This is for the purposes of example only; it should be understood that the scope of the invention is not limited to any particular transmission scheme, waveform, or telecommunications protocol but may be implemented in any transmission scheme that involves shaping the probability distribution of signals.

More detailed descriptions of the controller and the padding unit can be found below. First a general explanation is given about how the PCSM transmitter chain shown in Figure 1 operates.

An example of the steps performed by the various components in the transmitter chain are illustrated in Figure 4. A message is received in step S401 , which is to be prepared for transmission. First, a number of extra bits are optionally added to the message 109 that is to be transmitted (step S402). In the example of Figure 1 , kf bits are appended to the input message of length k bits. The appended bits could be generated by encoding message 109 with some error detection and/or error correction algorithm. For example, they could be the first kf bits of a CRC (of predefined length). Alternatively, they could just be known values, such as a string of zeros. The resulting sequence of length k'=k+kf is divided into two parts of lengths k_u and k_c, where k_u+k_c = k' (step S403). The lower branch (k_c bits) is input into the DM 103 (step S404). The parameters that control the operation of the DM are preferably derived from kc, n_c and m via a deterministic function. (The parameters k_c, n_c and m are described in more detail below).

The n_c symbols at the output of the DM, which are generally non-binary, are mapped to bits using Symbol-to-Bit mapper 104 (step S405). The Symbol-to-Bit mapper may be a deterministic mapper (e.g. a natural binary mapper). The resulting binary sequence has length nb.

The DM mapper 105 takes as input the k_u bits of the upper branch (which are uniformly distributed bits) and the nb bits from the output of the Symbol-to-Bit mapper (which are non-uniformly distributed bits) (steps S406 and S407). It then changes the order of the input bits (i.e. it interleaves them) so that they match the used channel code. This block can therefore be considered as an interleaver.

The output of the DM mapper 105 is then fed to an encoder (step S408). In one example the encoder may be a systematic FEC encoder with rate RFEC A systematic FEC encoder may produce a sequence of length n bits, consisting of nb+k_u systematic bits and p = n*(1 -RFEc) parity bits. At the output of the FEC encoder, the p parity bits and k_u systematic bits are uniformly distributed and the nb systematic bits have a nonuniform distribution. In another example, the encoder may be a partially systematic encoder, i.e, only a subset of the encoder input bits may appear in the encoder output.

The output of the FEC encoder is fed to the modulation interleaver 107, which rearranges the order of the bits for the symbol mapper 108 (step S409). The symbol mapper takes the rearranged bit sequence and assigns it to the modulation symbols (step S410). The modulation symbols could use any suitable modulation map, including 2^m-ary QAM, PAM etc. The modulation interleaver can also ensure that that the uniformly distributed bits (p+k_u in total) are used as the sign bits. The modulated signal is thus non-uniformly distributed but has uniformly distributed signs (the distribution of the channel input symbols 1 10 is symmetric). The controller 1 1 1 , 200 enables all relevant PSCM parameters to be obtained by specifying only the message length and the number of allocated channel units. If required, the transmitter can forward these two values to the receiver and the relevant parameters can be obtained at the receiver in the same way.

One example of a controller and its associated inputs and outputs is shown in Figure 5. This controller 501 is configured to calculate a series of parameters for controlling the transmitter chain shown in Figure 1 . The controller receives the message length k and the number of resource elements NRE as its inputs and calculates a set of appropriate PSCM parameters in a deterministic way. These parameters may include: kf: number of CRC bits (or filler bits) introduced by padding unit 1 12

k_u, k_c: demultiplexer output lengths

n_c: output length (in symbols) of DM 103

· m: modulation order

SE: spectral efficiency

RFEC: rate of the forward error correction code applied by encoder 106 n: code word length (in bits) The controller is not limited to calculating the parameters listed above and may be configured to calculate any relevant PCSM parameter. For example, the controller may also be configured to determine additional parameters for controlling the encoder 106, such as the lifting factor z and cyclic shifts for each element of the protograph matrix (base matrix) of a Quasi-Cyclic (QC) Low Density Parity Check (LDPC) code-based channel coding scheme.

The controller may be configured to generate the output parameters shown in Figure 5 as follows:

• Determine the spectral efficiency: SE = k NRE

· Determine whether or not to use PSCM in dependence on the shaping gain that is expected from using PCSM. This can be assessed by looking at the spectral efficiency for the message transmission. For example, if SE>=SE_min, where SEmin is a predefined threshold, the controller may determine that PSCM should be used. Otherwise, if the spectral efficiency is below the predefined threshold SEmin, the controller may determine that conventional BICM should be used. If the controller determines that PSCM is not appropriate, the steps described below are not required, since the PCSM parameters will not be needed.

· Determine the modulation order m and the FEC rate RFEC according to the calculated SE. The controller may have access to a look-up table for obtaining the appropriate values. For example:

If 1 <SE<=2 then m = 4 and RFEC = 112

If 2<SE<=4 then m = 6 and RFEC = 2/3

lf 4<SE<=6 then m = 8 and RFEC = 3/4

• Determine the FEC code word length n = ITI*N RE

• As an optional step, the controller may determine a set of additional parameters for the encoder. For example, if QC-LDPC codes are used as the channel code and the parity check matrix is defined as being a protograph matrix (base matrix) of size nrib x nb, the controller may be configured to determine the lifting factor z as: z=n/nb. The cyclic shift coefficients for each element of the protograph matrix can be determined by: (i) a look-up table depending on the value of z; or (ii) a deterministic function generating the cyclic shift coefficients according to z.

• Determine the DM output length n_c=ceil[2n/m]

· Determine k_u = ceil[n_c( 2-m(1 -RFEC))]

• Determine the DM input length k_c, such that: (i) k_c is maximized; and (ii) k_c <= k+kf,min - k_u is fulfilled, where kf,_min is a system constant that is defined in advance.

• Determine the number of filler bits kf = k_u + k_c - k Maximising k_c can depend on the particular DM since this often dictates the constraints of the maximisation. In general, one should try to set the other DM parameters (such as targeted distribution) in a way such that k_c is maximized. For example, if the DM is a CCDM and the target distribution of the output is a Maxwell-Boltzmann Distribution, such that: The aim is to try to find the optimal positive value of v such that k_c' = ccdm_initialize(P,n) is maximized. Here, 'ccdm_initialize' is a function that calculates the input length of a CCDM for given target distribution P and output length n. The parameter kf is one of the inputs to padding unit 1 12. The padding unit takes as input the message of length k and introduces kf filler bits such that the output length is k'=k+kf. In one example, kf is used to adjust the input to match a requirement of the DM. For example, a DM such as a CCDM does not work with all input message lengths. Instead, the DM input must match one of a predetermined set of acceptable input lengths. Previously this limited the message input length, but with padding unit 1 12 it becomes possible to use any message length and tailor it to the DM requirements. In other examples, kf is used to introduce extra error correction/detection ability. The filler bits may also have a dual-purpose and match the message length to the requirements of the DM at the same time as providing improved error detection/correction capability.

The task of kf,_min is to guarantee a minimum number of filler bits. The appropriate minimum may depend on the purpose of kf, which enables the padding unit to adjust the length of the message. The filler bits can either be known bits (such as zeros) or error detection/correction bits generated by optional encoder 303. If additional error detection/correction is unnecessary (e.g., so only known bits are used as filler bits), kf.min can be chosen as zero. kf,_min will usually only be greater zero if the filler bits are used not just for matching the input requirements of the DM, but also for some other reason (such as error detection/correction).

Optional encoder 303 may be configured to perform any suitable error correction/detection algorithm on the incoming message to generate the filler bits. The number of bits generated via this algorithm should be larger than or equal to kf, _min. In some implementations, the encoder will not introduce all the generated bits into the message, but only a subset. For example, the encoder may perform a CRC algorithm of predetermined length on the incoming message bits. The first kfof the resulting CRC bits may then be appended to the message. The missing CRC bits could cause some loss in performance, but this is compensated by the error detection/correction capabilities of DM. If error detection via CRC is not desired, then the padding unit 1 12 may just append kf known bits (for example, zeros) to the message.

The applicant hereby discloses in isolation each individual feature described herein and any combination of two or more such features, to the extent that such features or combinations are capable of being carried out based on the present specification as a whole in the light of the common general knowledge of a person skilled in the art, irrespective of whether such features or combinations of features solve any problems disclosed herein, and without limitation to the scope of the claims. The applicant indicates that aspects of the present invention may consist of any such individual feature or combination of features. In view of the foregoing description it will be evident to a person skilled in the art that various modifications may be made within the scope of the invention.

Claims

1 . A controller comprising:

an input configured to receive data that defines a length of a message to be transmitted, k, and a number of channel units, NRE, available for transmitting that message;

a parameter generator configured to determine, in dependence on k and NRE, one or more parameters for controlling an operation, which transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution, that will prepare the message for transmission.

2. A controller as claimed in claim 1 , wherein the parameter generator is configured to determine a parameter, in dependence on the data, which controls whether or not the message will be prepared for transmission by the operation.

3. A controller as claimed in any preceding claim, wherein the parameter generator is configured to generate each of the one or more parameters using a deterministic function.

4. A controller as claimed in any preceding claim, wherein the parameter generator is configured to generate parameters that define one or more of: a spectral efficiency associated with the transmission of the message; a modulation order; a code word length; a length of an input to a distribution matcher; a length of an output generated by the distribution matcher; a part of the message that is not to be input into the distribution matcher; a rate of an error correcting code; a length of one or more outputs generated by a demultiplexer; and a number of filler bits.

5. A method comprising:

receiving data that defines a length of a message to be transmitted, k, and a number of channel units, NRE, available for transmitting that message;

determining, in dependence on k and NRE, one or more parameters for controlling an operation, which transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution, that will prepare the message for transmission.

6. A padding unit configured to:

receive a message that is to be transmitted;

introduce a number of bits into that message; and

output the message and its introduced bits for processing by an operation, which transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution, that will prepare the message for transmission.

7. A padding unit as claimed in claim 6, wherein the number of bits is selected in dependence on an input message length associated with a distribution matcher that is configured to perform the operation.

8. A padding unit as claimed in claim 6 or 7, wherein the number of bits is selected in dependence on a desired rate of transmission of the message and/or in dependence on one or more parameters of a distribution matcher that is configured to perform the operation.

9. A padding unit as claimed in any of claims 6 to 7, wherein the number of bits is selected in dependence on a desired error detection and/or error correction performance.

10. A padding unit as claimed in any of claims 6 to 9, wherein the padding unit is configured to generate one or more of the number of bits in dependence on the message.

1 1 . A padding unit as claimed in claim 10, wherein the padding unit is configured to generate the one or more bits by applying a deterministic function to the message.

12. A padding unit as claimed in claim 10 or 1 1 , wherein the padding unit is configured to generate the one or more bits by encoding the message with an error detection and/or error correction algorithm.

13. A method comprising:

receiving a message that is to be transmitted;

introducing a number of bits into that message; and

outputting the message and its introduced bits for processing by an operation, which transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution, that will prepare the message for transmission.

14. A transmitter configured to:

receive a message that is to be transmitted;

determine an efficiency associated with the transmission of the message; and in dependence on the determined efficiency, select either a first transmit scheme, which includes an operation that transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution, or a second transmit scheme, which does not include the operation that transforms an original signal with a first probability distribution into a transformed signal with a second probability distribution, for preparing the message for transmission.

15. A transmitter as claimed in claim 14, wherein the transmitter is configured to select either the first transmit scheme or the second transmit scheme in dependence on a respective shaping gain that is expected to be achieved by each of the first and second transmit schemes at the determined efficiency.