CN102611465A - Coder of structured q-ary irregular repeat-accumulate code and coding method of coder - Google Patents

Abstract

The invention discloses a coder of a structured q-ary irregular repeat-accumulate (S-QIRA) code and a coding method of the coder, solving the problem that the existing coder of a q-ary irregular repeat-accumulate (QIRA) code is insufficient in parallelism and low in coding speed. The coder divides information symbol sequences to be coded into a plurality of subgroups; the symbol sequences in the subgroups are subjected to repetitive operation, interleaving operation, GF(q) weighting operation, merging operation and accumulation operation in sequence according to the groups; symbols in the same subgroup are processed in a parallel manner in each step and operated at the same time, and therefore, the degree of parallelism and the coding speed of the coder are effectively improved; and a produced check matrix of the S-QIRA code has a 'category' quasi-cycle structure, which can greatly reduce a memory unit for storing the check matrix of the coder and effectively reduce the complexity of hardware realization of the coder. The coder disclosed by the invention can be applied to correct the error in information transmission of a physical layer in a modern communication system.

Description

The structuring multiple irregular repeats to accumulate the encoder and the coding method of sign indicating number

Technical field

The invention belongs to communication technical field, particularly relate to a kind of encoder and coding method thereof of structuring multiple irregular RA code, can be used for the error control of physical layer data transmission.

Background technology

Low-density check LDPC sign indicating number is proposed in 1962 by Gallager the earliest, and MacKay, Neal equal nineteen ninety-five the LDPC sign indicating number has been carried out " finding " again, and have proved that its code length has the error control performance of approaching the Shannon limit when being tending towards infinite.1998, Davey and MacKay were generalized to high-order limited territory GF (q) with binary LDPC sign indicating number, on q＞2.Extensive studies shows, is superior to binary LDPC sign indicating number and Turbo code based on the multielement LDPC code of GF (q) in short-and-medium code length performance.Particularly, multielement LDPC code is compared binary LDPC sign indicating number has following advantage: 1) multielement LDPC code has stronger antiburst error ability; 2) multielement LDPC code has lower wrong flat bed; 3) multielement LDPC code is preferably combines with High Order Modulation System; Yet initial multielement LDPC code is defined on the sparse check matrix of random configuration, so its encoder complexity is very high.In order to address this problem, but the multielement LDPC code that needs structure to have fast coding structure and error control function admirable.

But in the multielement LDPC code structural scheme of numerous fast codings, multiple irregular repeats accumulation, and (Q-ary Irregular Repeat-Accumulate, QIRA) sign indicating number can carry out simple fast coding through repetition and accumulating operation.Such yard combines the low encoder complexity of Turbo code and the good parallel iteration decoding performance of multielement LDPC code.Fig. 1 has shown the coder structure of QIRA sign indicating number, comprising duplication code, weighter, symbol interleaver, combiner, accumulator and multiplexer six parts.Visible by Fig. 1, the QIRA sign indicating number can be accomplished the low complex degree coding through the mode of serially concatenated.Suppose that code length is that the information symbol length of the QIRA sign indicating number of N is K, checking symbol length is M, and then its specific coding process comprises the steps:

1) the symbol u among the input information symbol sebolic addressing u _i, i=1 ..., K repeats r by duplication code _iInferior, obtain symbol sebolic addressing v;

2) each symbol carries out the weighting of GF (q) multiplication by weighter among the symbol sebolic addressing v; Carry out sequence by symbol interleaver subsequently and interweave, obtain output symbol sequence

3) symbol sebolic addressing

Press coefficient a by combiner by symbol _i, i=1 ..., M carries out union operation, obtains the long symbol sebolic addressing w of M that is;

4) accumulator adds up and ranking operation to each symbol among the w, and the length of output is the checking symbol sequence that the symbol sebolic addressing p of M is encoder;

5) multiplexer information symbol sequence u and checking symbol sequence p are carried out multiplexing, obtain encoder final output QIRA sign indicating number code word c=(u, p);

Each computing all is defined on the finite field gf (q) in the above cataloged procedure.The check matrix H of the QIRA sign indicating number that is generated by this coded system is made up of two parts: H=[H _u, H _p], H wherein _uPart has random structure, H _pPart is:

The factor graph of the QIRA sign indicating number that generates is as shown in Figure 2, and its decoding then can be carried out parallel iteration decoding, m=r among Fig. 2 on this factor graph ₁+ r ₂

In sum, the QIRA sign indicating number can carry out fast coding through cascade duplication code and convolution code as serial concatenation of codes is the same, can on its factor graph, carry out parallel iteration decoding to obtain good performance as multielement LDPC code is the same simultaneously.

Yet the encoder of described traditional Q IRA sign indicating number and coding method lack certain concurrency, thereby have influenced its coding rate.And the QIRA sign indicating number that this coding method generates lacks structural, thereby is unfavorable for the storage and the realization of High Speed of decoder.

Summary of the invention

The objective of the invention is to overcome the encoder of above-mentioned traditional Q IRA sign indicating number and the deficiency of coding method; Provide a kind of structuring multiple irregular to repeat to accumulate the encoder and the corresponding encoded method of S-QIRA sign indicating number; To improve the concurrency and the coding rate of encoder; And the S-QIRA sign indicating number that makes generation has ' class ' accurate loop structure characteristic, thereby storage and the hardware of simplifying corresponding decoder are realized.

For realizing above-mentioned purpose, encoder of the present invention comprises:

The grouping duplicator: be used to accomplish the grouping repetitive operation to symbol sebolic addressing, wherein every group length is s;

Class symbol interleaver: in order to accomplish block interleaved operation to symbol sebolic addressing;

Grouping GF (q) weighter I: in order to accomplish symbol sebolic addressing is carried out the packet-weighted operation by GF (q) nonzero element, wherein every group of internal symbol adopts same weight coefficient;

The grouping combiner: in order to accomplish the grouping union operation to symbol sebolic addressing, the every group code that wherein generates adopts the merge coefficient that equates;

Grouping accumulator: in order to symbol sebolic addressing is sorted, and the symbol sebolic addressing after the ordering divided into groups to carry out the operation that adds up of weighted sum on the GF (q);

Multiplexer: in order to two symbol sebolic addressing serials are multiplexed with 1 symbol sebolic addressing;

Above each several part is serially connected from top to bottom, accomplishes the serial code operation to information symbol sequence.

Described grouping accumulator comprises:

Sorting unit, grouping GF (q) weighter II, register and GF (q) adder unit; The input of grouping accumulator directly gets into sorting unit; Sorting unit exports GF (q) adder unit to after accomplishing the sorting operation to symbol sebolic addressing; GF (q) adder unit carries out GF (q) add operation to the output of sorting unit and grouping GF (q) weighter II, and its output gets into grouping GF (q) weighter II through register simultaneously as the output of grouping accumulator; Feedback inputed to GF (q) adder unit after grouping GF (q) weighter II carried out packet-weighted to symbol sebolic addressing by GF (q) nonzero element, and wherein GF (q) expression size is the finite field of q.

For realizing above-mentioned purpose, coding method of the present invention comprises the steps:

(1) grouping repeating step:

To code length is that N, information symbol length are that K, checking symbol length are that the multiple irregular of M=N-K repeats the accumulation sign indicating number and encodes, promptly at first with information symbol sequence u=(u to be encoded ₀, u ₁..., u _K-1) be divided into long k=K/s the grouping U of s of being ⁽⁰⁾..., U ^(k-1), again by organizing to each grouping U ^(l)In symbol

Carry out repetition, 0≤l＜k wherein, on the same group in each symbol Number of repetition be r _l, make r=(r ₁+ ...+r _K-1)/k then obtains the long replicator sequence v of rK that is for the average number of repetition of all symbols is r:

(2) block interleaved step:

2a) the accurate cyclic check matrix H of definition encoder pairing ' class '=[H _u, H _p], H wherein _uBe information matrix array, H _pBe a burst of row of biconjugate angular moment, represent as follows:

In the formula

The expression size is the unit matrix I of s _sEach row is cyclic shift B to the right _{I, j}The inferior square formation that obtains, δ _{I, j}Nonzero element on the expression GF (q), 0≤i≤m-1,0≤j≤k-1;

In the formula 0 _sThe expression size is complete zero square formation of s, γ _iBe the nonzero element on the GF (q),

The expression size is the square formation of s:

2b) make a _iThe i every trade of information matrix array is heavy in the pairing check matrix H of presentation code device, h _{I, j}For the i of this matrix array capable in the row mark of j non-zero cyclic shift matrices, b _{I, j}Be the cyclic shift coefficient of this cyclic shift matrices, then the definition interweave the subscript sequence (π (0) ..., π (rK-1))=(π ₀, π ₁..., π _M-1), m=M/s wherein,

π _i＝(π _i(0)，π _i(1)，...，π _i(s-1))，0≤i≤m-1，

${\mathrm{\π}}_i\left(t\right)=({\mathrm{sh}}_{i,0}+(b_{i,0}+t)\mathrm{mod}s...,{\mathrm{sh}}_{i,a_i-1}+(b_{i,a_i-1}+t)\mathrm{mod}s),0\≤t\≤s-1,$

2c) replicator sequence v is carried out block interleaved, obtain the interleaved symbol sequence according to the above-mentioned subscript sequence that interweaves

$\stackrel{\‾}{v}=({\stackrel{\‾}{v}}_1,...,{\stackrel{\‾}{v}}_{\mathrm{rK}-1})=(u_{\mathrm{\π}\left(0\right)},u_{\mathrm{\π}\left(1\right)},...,u_{\mathrm{\π}(\mathrm{rK}-1)});$

(3) grouping GF (q) weighting step:

3a) make β represent the weight coefficient sequence, β be divided into the individual long grouping of s that is of m=M/s:

Wherein

is the i of the pairing information matrix array of encoder GF (q) the nonzero element sequence in capable, and wherein GF (q) expression size is the finite field of q;

3b) each item among each item

in the interleaved symbol sequence

and the weight coefficient sequence β is multiplied each other in order in twos, obtain weighted symbol sequence

(4) grouping combining step:

4a) make A _dThe d every trade of the pairing information matrix of presentation code device is heavy, 0≤d≤M-1, definition merge coefficient sequence A=(A ₀..., A _M-1), A wherein ₀+ A ₁+ ... + A _M-1=rK;

4b) to the weighted symbol sequence

In each symbol Merge successively by each item in the merge coefficient sequence A, obtain the long merging symbol sebolic addressing w=(w of M that is ₀..., w _M-1), wherein

${\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">w</figure-callout>}}_0={\hat{v}}_0+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{A_0-1}$

${\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA0000151120100000032.png"\; state="\{\{state\}\}">w</figure-callout>}}_1={\hat{v}}_{A_0}+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{{\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_0+A_1-1}$

$\begin{array}{c}.\\ .\\ .\end{array};$

$w_{M-1}={\hat{v}}_{{\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_0+{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="HDA0000151120100000032.png"\; state="\{\{state\}\}">A</figure-callout>}}_1+\&CenterDot;\&CenterDot;\&CenterDot;+A_{M-2}}+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{{\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_0+A_1+\&CenterDot;\&CenterDot;\&CenterDot;+A_{M-1}-1}$

(5) grouping accumulation step:

5a) will merge each symbol w among the symbol sebolic addressing w ₀..., w _M-1Sort by following order:

((w ₍₀₎，...，w _(0)+(m-1)s)，...，(w _(s-1)，w _(s-1)+s，...，w _(s-1)+(m-1)s))，

This sequence is ordering symbol sebolic addressing

5b) right

Carry out accumulating operation, be about to

Middle symbol

Through register and after GF (q) weighting again with symbol Add up, obtain symbol p _d, wherein 0＜d≤M-1, and then the living checking symbol sequence p=(p that grows into M ₀..., p _M-1);

(6) multiplexer information symbol sequence u and checking symbol sequence p are carried out multiplexing, obtain encoder long for the final output code word c=of N (u, p).

The present invention has following advantage:

Encoder of the present invention is owing to be divided into some groupings with information symbol sequence to be encoded; Again to the symbol sebolic addressing after dividing into groups by group divide into groups successively repetition, block interleaved, grouping GF (q) weighting, divide into groups to merge, the grouping accumulating operation; And in each step, all the symbol in the same grouping is carried out parallel processing, effectively raise the degree of parallelism of encoder; Because encoder carries out computing simultaneously to every group of internal symbol, further improved coding rate simultaneously; Because the check matrix H of the S-QIRA sign indicating number that coding method of the present invention generates has ' class ' accurate loop structure, not only significantly reduce the required memory cell of decoder this check matrix of storage in addition, and effectively reduced the hardware implementation complexity of decoder.

Simulation result shows that the S-QIRA sign indicating number based on GF (64) that encoder that is proposed and specific coding method generate all has good error control performance under BPSK-AWGN channel and 64QAM-Rayleigh fading channel.

Below in conjunction with accompanying drawing the present invention is elaborated.

Description of drawings

Fig. 1 is the coder structure block diagram of traditional Q IRA sign indicating number;

Fig. 2 is the factor graph of traditional Q IRA sign indicating number;

Fig. 3 is the coder structure of S-QIRA sign indicating number of the present invention;

Fig. 4 is the coding flow chart of S-QIRA sign indicating number of the present invention;

Fig. 5 is the analogous diagram of S-QIRA sign indicating number of the present invention on the BPSK-AWGN channel;

Fig. 6 is the analogous diagram of S-QIRA sign indicating number of the present invention on the 64QAM-Rayleigh fading channel.

Embodiment

With reference to Fig. 3, the encoder that the structuring multiple irregular that the present invention proposes repeats to accumulate sign indicating number comprises: grouping duplicator, class symbol interleaver, grouping GF (q) weighter, grouping combiner, grouping accumulator and multiplexer six parts.Wherein, the input information symbol sebolic addressing u of encoder directly gets into the grouping duplicator, accomplishes the grouping repetitive operation to u by the grouping duplicator, and every group length is s, obtains replicator sequence v; The class symbol interleaver carries out the block interleaved operation to the output symbol sequence v of grouping duplicator; It is output as interleaved symbol sequence

grouping GF (q) weighter interleaved symbol sequence

is carried out the packet-weighted operation by GF (q) nonzero element; Wherein every group of internal symbol adopts same weight coefficient; Union operation divides into groups to weighted symbol sequence

to obtain weighted symbol sequence

grouping combiner; The every group code that generates adopts the merge coefficient that equates, its output merges symbol sebolic addressing w and is connected to the grouping accumulator; The grouping accumulator comprises: sorting unit, the GF that adds up (q) weighter, register and GF (q) adder unit four parts.This sorting unit exports GF (q) adder unit to after accomplishing the sorting operation to symbol sebolic addressing; This GF (q) adder unit carries out GF (q) add operation to the sorting unit and the output of GF (q) weighter that adds up; Its output is the checking symbol sequence p of grouping accumulator output; Checking symbol sequence p gets into GF (q) weighter that adds up through register simultaneously; Feedback inputed to GF (q) adder unit after this GF that adds up (q) weighter was carried out packet-weighted to each item among the p by GF (q) nonzero element, and above-mentioned symbol GF (q) expression size is the finite field of q; It is multiplexing that multiplexer carries out serial to information symbol sequence u and checking symbol sequence p, obtain encoder final output code word c=(u, p).

With reference to Fig. 4, utilize above-mentioned encoder to encode, comprise the steps:

Step 1, to the information symbol sequence repetitive operation of dividing into groups:

1a) divide into groups to divide:

To code length is that N, information symbol length are that K, checking symbol length are that the multiple irregular of M=N-K repeats the accumulation sign indicating number and encodes, promptly at first with information symbol sequence u=(u to be encoded ₀, u ₁..., u _K-1) be divided into long k=K/s the grouping U of s of being ⁽⁰⁾..., U ^(k-1),

Wherein:

$U^{\left(l\right)}=(U_0^{\left(l\right)},...,U_{s-1}^{\left(l\right)}),0\&le;l<k;$

1b) symbol repeats:

Pursue group according to l=0,1 ..., the order of k-1 is to each U that divides into groups ^(l)In symbol

Carry out repetition, on the same group in each symbol

Number of repetition all be made as rl, make r _l=(r ₀+ ...+r _K-1)/k is the average number of repetition of all symbols, then obtains the long replicator sequence v of rK that is:

Step 2, the replicator sequence is carried out the block interleaved operation:

2a) definition check matrix:

The accurate cyclic check matrix H of definition encoder pairing ' class '=[H _u, H _p], H wherein _uBe information matrix array, H _pBe a burst of row of biconjugate angular moment, represent as follows:

δ in the formula _{I, j}Field element on the expression GF (q), 0≤i≤m-1,0≤j≤k-1, The expression size is the unit matrix I of s _sEach row is cyclic shift B to the right _{I, j}The inferior square formation that obtains, for example B _{I, j}=1 o'clock:

In the formula 0 _sThe expression size is complete zero square formation of s, γ _iBe the nonzero element on the GF (q),

The expression size is the square formation of s:

2b) define the subscript sequence that interweaves:

Make a _iInformation matrix array H in the pairing check matrix H of presentation code device _uThe i every trade heavy, h _{I, j}For the i of this matrix array capable in the row mark of j non-zero cyclic shift matrices, b _{I, j}Be the cyclic shift coefficient of this cyclic shift matrices, then the definition interweave the subscript sequence (π (0) ..., π (rK-1))=(π ₀, π ₁..., π _M-1), m=M/s wherein,

π _i＝(π _i(0)，π _i(1)，...，π _i(s-1))，0≤i≤m-1，

${\mathrm{\&pi;}}_i\left(t\right)=({\mathrm{sh}}_{i,0}+(b_{i,0}+t)\mathrm{mod}s,...,{\mathrm{sh}}_{i,a_i-1}+(b_{i,a_i-1}+t)\mathrm{mod}s),0\&le;t\&le;s-1;$

2c) block interleaved:

According to the above-mentioned subscript sequence that interweaves replicator sequence v is carried out block interleaved, obtain the interleaved symbol sequence

$\stackrel{\&OverBar;}{v}=({\stackrel{\&OverBar;}{v}}_1,...,{\stackrel{\&OverBar;}{v}}_{\mathrm{rK}-1})=(u_{\mathrm{\&pi;}\left(0\right)},u_{\mathrm{\&pi;}\left(1\right)},...,u_{\mathrm{\&pi;}(\mathrm{rK}-1)}).$

Step 3, the interleaved symbol sequence is carried out GF (q) operation for weighting:

3a) definition weight coefficient sequence:

Make β represent the weight coefficient sequence, β be divided into the individual long grouping of s that is of m=M/s:

Wherein

is the i of the pairing information matrix array of encoder GF (q) the nonzero element sequence in capable, and wherein GF (q) expression size is the finite field of q;

3b) sequence multiplies each other:

Each item among each item in the interleaved symbol sequence

and the weight coefficient sequence β is multiplied each other in order in twos, obtain weighted symbol sequence

Step 4, to the weighted symbol sequence union operation that divides into groups:

4a) definition merge coefficient sequence:

Make A _dThe d every trade of the pairing information matrix of presentation code device is heavy, 0≤d≤M-1, definition merge coefficient sequence A=(A ₀..., A _M-1), A wherein ₀+ A ₁+ ... + A _M-1=rK;

4b) symbol merges:

To the weighted symbol sequence

In each symbol

Merge successively by each item in the merge coefficient sequence A, obtain the long merging symbol sebolic addressing w=(w of M that is ₀..., w _M-1), wherein

${\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">w</figure-callout>}}_0={\hat{v}}_0+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{A_0-1}$

${\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA0000151120100000032.png"\; state="\{\{state\}\}">w</figure-callout>}}_1={\hat{v}}_{{\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_0}+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{{\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_0+A_1-1}$

......

$w_{M-1}={\hat{v}}_{{\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_0+A_1+\&CenterDot;\&CenterDot;\&CenterDot;+A_{M-2}}+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{{\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_0+A_1+\&CenterDot;\&CenterDot;\&CenterDot;+A_{M-1}-1};$

Step 5 is combined the symbol sebolic addressing operation of dividing into groups to add up:

5a) be combined each symbol w among the symbol sebolic addressing w ₀..., w _M-1Sort, obtain the symbol sebolic addressing that sorts $\stackrel{\&OverBar;}{w}=({\stackrel{\&OverBar;}{w}}_0,...,{\stackrel{\&OverBar;}{w}}_{M-1}),$ Wherein:

$({\stackrel{\&OverBar;}{w}}_0,...,{\stackrel{\&OverBar;}{w}}_{M-1})=((w_{\left(0\right)},...,w_{\left(0\right)+(m-1)s}),...,(w_{(s-1)},w_{(s-1)+s},...,w_{(s-1)+(m-1)s}));$

5b) to the ordering symbol sebolic addressing

Carry out accumulating operation, be about to

Middle symbol Through register and after GF (g) weighting again with symbol

Add up, obtain symbol p _d, wherein 0＜d≤M-1, and then the living checking symbol sequence p=(p that grows into M ₀..., p _M-1), be specially:

${\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_0={\stackrel{\&OverBar;}{w}}_0$

$p_s={\mathrm{\&gamma;}}_0{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000151120100000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_0+{\stackrel{\&OverBar;}{w}}_1$

......

$p_{(m-1)s}={\mathrm{\&gamma;}}_{m-2}{p}_{(m-2)s}+{\stackrel{\&OverBar;}{w}}_{m-1}$

For i=1,2 ..., s-1 then has

$p_i={\mathrm{\&gamma;}}_{m-1}{p}_{i-1+(m-1)s}+{\stackrel{\&OverBar;}{w}}_{\mathrm{mi}}$

$p_{i+s}={\mathrm{\&gamma;}}_0{p}_i+{\stackrel{\&OverBar;}{w}}_{\mathrm{mi}+1}$

......

$p_{i+(m-1)s}={\mathrm{\&gamma;}}_{m-2}{p}_{i+(m-2)s}+{\stackrel{\&OverBar;}{w}}_{m(i+1)-1}$

γ wherein ₀, γ ₁..., γ _M-2Be a burst of row of biconjugate angular moment H _pMiddle GF (g) nonzero element.

Step 6, information symbol sequence and checking symbol sequence are carried out multiplexing operation:

Multiplexer carries out information symbol sequence u and checking symbol sequence p multiplexing, is about to u and is serially connected with p, obtain encoder grow for the final output code word c=of N (u, p).

The present invention proposes the S-QIRA code performance and can further specify through following emulation:

Simulation parameter: the S-QIRA sign indicating number that emulation of the present invention is selected for use is based on finite field gf (64), its code length be 84 symbols promptly 504 bits, code check be 1/2, cyclic shift matrices size s=7.Simultaneously, choose code length, binary low-density check BLDPC sign indicating number that code check is all identical with this S-QIRA sign indicating number carries out performance relatively.Wherein, the S-QIRA sign indicating number adopts the minimum and EMS decoding algorithm of polynary sum-product algorithm QSPA and expansion respectively, and the BLDPC sign indicating number then adopts belief propagation BP decoding algorithm.

The emulation content:

Emulation one: S-QIRA sign indicating number of the present invention and the FER BLER performance of existing BLDPC sign indicating number under the BPSK-AWGN channel are carried out Computer Simulation, and simulation result is seen Fig. 5.

Emulation two: S-QIRA sign indicating number of the present invention and the BLER performance of existing BLDPC sign indicating number under the 64QAM-Rayleigh fading channel are carried out Computer Simulation, and simulation result is seen Fig. 6.

Analysis of simulation result:

Visible from Fig. 5, on the BPSK-AWGN channel, when S-QIRA sign indicating number of the present invention was 10-4 in the BLER of system performance, its signal to noise ratio Eb/N0 was superior to the about 0.43dB of BLDPC sign indicating number.

Visible from Fig. 6, on the 64QAM-Rayleigh fading channel, when S-QIRA sign indicating number of the present invention was 10-4 in the BLER of system performance, its signal to noise ratio Eb/N0 was superior to the about 3.7dB of BLDPC sign indicating number.

The present invention not detailed description is a technology as well known to those skilled in the art.

Claims (3)

1. a structuring multiple irregular repeats to accumulate the encoder of sign indicating number, comprising:

The grouping duplicator: be used to accomplish the grouping repetitive operation to symbol sebolic addressing, wherein every group length is s;

Class symbol interleaver: in order to accomplish block interleaved operation to symbol sebolic addressing;

Grouping GF (q) weighter: in order to accomplish symbol sebolic addressing is carried out the packet-weighted operation by GF (q) nonzero element, wherein every group of internal symbol adopts same weight coefficient;

The grouping combiner: in order to accomplish the grouping union operation to symbol sebolic addressing, the every group code that wherein generates adopts the merge coefficient that equates;

Grouping accumulator: in order to symbol sebolic addressing is sorted, and the symbol sebolic addressing after the ordering divided into groups to carry out the operation that adds up of weighted sum on the GF (q);

Multiplexer: in order to two symbol sebolic addressing serials are multiplexed with 1 symbol sebolic addressing;

Above each several part is serially connected from top to bottom, accomplishes the serial code operation to information symbol sequence.

2. encoder according to claim 1, wherein said grouping accumulator comprises:

Sorting unit, the GF that adds up (q) weighter, register and GF (q) adder unit; Sorting unit exports GF (q) adder unit to after accomplishing the sorting operation to symbol sebolic addressing; GF (q) adder unit carries out GF (q) add operation to the output of sorting unit and grouping GF (q) weighter II; Its output is as the output of grouping accumulator; Get into grouping GF (q) weighter II through register simultaneously, feedback inputed to GF (q) adder unit after grouping GF (q) weighter II carried out packet-weighted to symbol sebolic addressing by GF (q) nonzero element, and wherein GF (q) expression size is the finite field of q.

3. a structuring multiple irregular repeats to accumulate the coding method of sign indicating number, comprising:

(1) grouping repeating step:

To code length is that N, information symbol length are that K, checking symbol length are that the multiple irregular of M=N-K repeats the accumulation sign indicating number and encodes, promptly at first with information symbol sequence u=(u to be encoded ₀, u ₁..., u _K-1) be divided into long k=K/s the grouping U of s of being ⁽⁰⁾..., U ^(k-1), again by organizing to each grouping U ^(l)In symbol

Carry out repetition, 0≤l＜k wherein, on the same group in each symbol

Number of repetition be r _l, make r=(r ₀+ ...+r _K-1)/k is the average number of repetition of all symbols, then obtains the long replicator sequence v of rK that is:

(2) block interleaved step:

2a) the accurate cyclic check matrix H of definition encoder pairing ' class '=[H _u, H _p], H wherein _uBe information matrix array, H _pBe a burst of row of biconjugate angular moment, represent as follows:

In the formula

The expression size is the unit matrix I of s _sEach row is cyclic shift B to the right _{I, j}The inferior square formation that obtains, δ _{I, j}Field element on the expression GF (q), 0≤i≤m-1,0≤j≤k-1;

In the formula 0 _sThe expression size is complete zero square formation of s, γ _iBe the nonzero element on the GF (q),

The expression size is the square formation of s:

2b) make a _iInformation matrix array H in the pairing check matrix H of presentation code device _uThe i every trade heavy, h _{I, j}For the i of this matrix array capable in the row mark of j non-zero cyclic shift matrices, b _{I, j}Be the cyclic shift coefficient of this cyclic shift matrices, then the definition interweave the subscript sequence (π (0) ..., π (rK-1))=(π ₀, π ₁..., π _M-1), m=M/s wherein,

π _i＝(π _i(0)，π _i(1)，...，π _i(s-1))，0≤i≤m-1，

${\mathrm{\&pi;}}_i\left(t\right)=({\mathrm{sh}}_{i,0}+(b_{i,0}+t)\mathrm{mod}s,...,{\mathrm{sh}}_{i,a_i-1}+(b_{i,a_i-1}+t)\mathrm{mod}s),0\&le;t\&le;s-1,$

2c) replicator sequence v is carried out block interleaved, obtain the interleaved symbol sequence according to the above-mentioned subscript sequence that interweaves

$\stackrel{\&OverBar;}{v}=({\stackrel{\&OverBar;}{v}}_1,...,{\stackrel{\&OverBar;}{v}}_{\mathrm{rK}-1})=(u_{\mathrm{\&pi;}\left(0\right)},u_{\mathrm{\&pi;}\left(1\right)},...,u_{\mathrm{\&pi;}(\mathrm{rK}-1)});$

(3) grouping GF (q) weighting step:

3a) make β represent the weight coefficient sequence, β be divided into the individual long grouping of s that is of m=M/s:

Wherein

Be the pairing information matrix array of encoder H _uGF (q) the nonzero element sequence of i in capable, wherein GF (q) expression size is the finite field of q;

3b) each item among each item

in the interleaved symbol sequence and the weight coefficient sequence β is multiplied each other in order in twos, obtain weighted symbol sequence

(4) grouping combining step:

4a) make A _dThe d every trade of the pairing information matrix of presentation code device is heavy, 0≤d≤M-1, definition merge coefficient sequence A=(A ₀..., A _M-1), A wherein ₀+ A ₁+ ...+A _M-1=rK;

4b) to the weighted symbol sequence

In each symbol

Merge successively by each item in the merge coefficient sequence A, obtain the long merging symbol sebolic addressing w=(w of M that is ₀..., w _M-1), wherein

$w_0={\hat{v}}_0+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{A_0-1}$

$w_1={\hat{v}}_{A_0}+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{A_0+A_1-1}$

......

$w_{M-1}={\hat{v}}_{A_0+A_1+\&CenterDot;\&CenterDot;\&CenterDot;+A_{M-2}}+\&CenterDot;\&CenterDot;\&CenterDot;+{\hat{v}}_{A_0+A_1+\&CenterDot;\&CenterDot;\&CenterDot;+A_{M-1}-1};$

(5) grouping accumulation step:

5a) be combined each symbol w among the symbol sebolic addressing w ₀..., w _M-1Sort, obtain the symbol sebolic addressing that sorts $\stackrel{\&OverBar;}{w}=({\stackrel{\&OverBar;}{w}}_0,...,{\stackrel{\&OverBar;}{w}}_{M-1}),$ Wherein:

$({\stackrel{\&OverBar;}{w}}_0,...,{\stackrel{\&OverBar;}{w}}_{M-1})=((w_{\left(0\right)},...,w_{\left(0\right)+(m-1)s}),...,(w_{(s-1)},w_{(s-1)+s},...,w_{(s-1)+(m-1)s}));$

5b) right

Carry out accumulating operation, be about to

Middle symbol

Through register and after GF (q) weighting again with symbol

Add up, obtain symbol p _d, wherein 0＜d≤M-1, and then the living checking symbol sequence p=(p that grows into M ₀..., p _M-1);

(6) multiplexer carries out information symbol sequence u and checking symbol sequence p multiplexing, is about to u and is serially connected with p, obtain encoder grow for the final output code word c=of N (u, p).

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