CN111726123B - Rate-free multi-user coding method suitable for interweaving multi-address access system - Google Patents

Rate-free multi-user coding method suitable for interweaving multi-address access system Download PDF

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CN111726123B
CN111726123B CN202010611097.5A CN202010611097A CN111726123B CN 111726123 B CN111726123 B CN 111726123B CN 202010611097 A CN202010611097 A CN 202010611097A CN 111726123 B CN111726123 B CN 111726123B
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王雪蕾
李颖
张怡菲
侯伟
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Xidian University
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    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • H03M13/1162—Array based LDPC codes, e.g. array codes
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Abstract

The invention discloses a non-rate multi-user coding method suitable for an interleaved multi-access system, which mainly solves the problems of overhigh system complexity and poor decoding performance in the prior art. The implementation scheme is as follows: generating an initial sequence for each user; carrying out outer encoder encoding on the initial sequence of each user to obtain an outer encoder encoding sequence; carrying out inner encoder encoding on the outer encoder encoding sequence to obtain an inner encoder encoding sequence; interweaving the coding sequence of the inner encoder to obtain an interweaved sequence; modulating the interleaved sequence to obtain a modulated sequence; inputting the modulation sequences of all users into a Gaussian multi-user channel to obtain an output sequence; and decoding the output sequence and outputting the decoded sequence. The invention reduces the complexity of the system by cascading a fixed external space coupling repeated accumulation code with an adjustable internal repeated code, improves the decoding performance in any rate range, and can be used for an interleaving multiple access system.

Description

Rate-free multi-user coding method suitable for interweaving multi-address access system
Technical Field
The invention belongs to the technical field of communication, and further relates to a rateless multi-user coding method which can be used for an IDMA system.
Background
The interleaved multiple access IDMA system is a standard scheme for overload scenarios in 5G networks. At the transmitting end, all users use the same coding method, i.e. single user code concatenates the same spreading code. At the receiving end, different users are distinguished by different interleavers. Compared with other multiple access technologies, the IDMA scheme has the advantages of high spectrum utilization rate, performance close to the theoretical limit, and low cost for multi-user MUD detection. Many efforts have been made by researchers to combat multi-user interference and ensure the reliability of communications.
Song et al, in its published paper "Maximum sum rate of repeat-accumulation system by fixed-point analysis" (IEEE Transactions on Communications,2012, 3011-3022), propose a regular, repeated, accumulated RA code and concatenate it with spreading codes, but this scheme only works well at certain low rate points.
In order to obtain good performance at more rate points, g.song et al used parallel concatenated codes PCC in the paper "K-User parallel coordinated code for Gaussian multiple-access channel" (IEEE International Conference Communications (ICC), 2013, 3286-3291), but did not consider the complexity problem of coding too much.
In order to reduce the complexity of the coding, g.song et al in the paper "a low-complexity multi-user coding scheme with near-capacity performance" (IEEE Transactions on Vehicular Technology,2017, 6775-6786) proposed an irregular repeat and accumulate code based on repeat assistance for low-rate areas, but this scheme has a low reliability of information transmission.
To further improve transmission reliability, y.chi et al applied the spatially coupled SC technique in its published paper "partial duplicated SC-LDPC codes for multiple-access channels" (IEEE Communications Letters,2016, 3286-3291), constructing a more generic spatially coupled multiuser code, referred to as Partially repeated spatially coupled low density parity check PR-SC-LDPC code. This scheme, while providing near shannon-limited iterative decoding performance over an arbitrary rate range, still has high system complexity.
The above-mentioned multi-user coding schemes require different encoder and decoder implementations for different rates, resulting in high system complexity, since they are designed and optimized for individual and rate points.
Disclosure of Invention
The present invention aims to overcome the defects of the prior art and design a rateless multi-user code suitable for an interleaving multi-access system. The complexity of the system is reduced, and the decoding performance is further improved in an arbitrary speed range.
The technical idea of the invention is as follows: the fixed outer space coupling repeated accumulation SC-RA encoding and the adjustable inner repeated encoding are cascaded, and the SC-RA encoding is selected as the outer encoding to meet the requirement of high decoding performance; by selecting the repetition code as the inner code, the no-rate characteristic is satisfied. The concrete implementation comprises the following steps:
1. a rateless multi-user coding method for use in an interleaved multiple access IDMA system, comprising:
(1) Generating an initial sequence u for each user in an IDMA system;
(2) Carrying out outer SC-RA coding on the initial sequence u to obtain an outer coder coding sequence c j ：
(2a) Equally dividing the initial sequence u into L segmented sequences u i ,i＝0,1,...,L-1；
(2b) For each segmented sequence u i Performing a first rearrangement operation to obtain rearranged sequences
Figure BDA0002562180780000021
Figure BDA0002562180780000022
Wherein Q represents the number of subsequences of the rearranged sequence, u i,q Representing the ith sequence of segments u i Q =0,1, ·, Q-1;
(2c) Each segmentation sequence u i Rearranged subsequence u of i,q Respectively carrying out modulo-2 addition (i + q) times to obtain a combined sequence t j ：
Figure BDA0002562180780000023
Wherein u is j-q,q Representing a segmented sequence u j-q The q-th rearranged subsequence of (1);
(2d) For combined sequence t j Performing accumulation operation to obtain the coding sequence c of the outer encoder j ：
Figure BDA0002562180780000024
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002562180780000025
representing outer encoder code sequences c j Q =0,1,.., L + Q-2;
(3) Coding sequence c of external encoder j And (3) carrying out internal repeated code coding to obtain an internal coder coding sequence c:
(3a) Each of the segmentation sequences u of pair (2 a) i And respectively carrying out second rearrangement operation to obtain a first sequence:
Figure BDA0002562180780000031
where α denotes each segment sequence u i The number of the sub-sequences of (a),
Figure BDA0002562180780000032
represents the mth subsequence of the first sequence, m =0,1, ·, L-1;
(3b) The outer encoder code sequence c of (2 d) j Each sequence of (1)
Figure BDA0002562180780000033
And (3) respectively carrying out rearrangement operation to obtain a second sequence:
Figure BDA0002562180780000034
wherein β represents each sequence
Figure BDA0002562180780000035
Number of sub-sequences of (4), based on the comparison result>
Figure BDA0002562180780000036
An nth subsequence representing a second sequence, n =0,1, ·, L + Q-2;
(3c) Combining the first sequence v in (3 a) and the second sequence p in (3 b) according to the sequence to obtain the coding sequence of the inner encoder
Figure BDA0002562180780000037
(4) Interweaving the coding sequence c of the inner coder to obtain an interweaving sequence pi;
(5) Carrying out binary phase shift keying BPSK modulation on the interleaved sequence pi, and modulating a 01 sequence to be modulated into a +/-1 sequence to obtain a modulation sequence x;
(6) Inputting the modulation sequence x into a Gaussian multi-user channel to obtain an output sequence y;
(7) And decoding the output sequence y and outputting a decoded sequence.
Compared with the prior art, the invention has the following advantages:
firstly, the invention adopts the fixed SC-RA code as the outer code, thereby overcoming the problem that the outer code of the prior art can not approach the Shannon limit of a continuous rate region, and leading the invention to have a simpler system encoder and high decoding performance in any rate range;
secondly, the invention adopts the repeated code with adjustable parameters as the internal code, and the non-rate characteristic can be met by adjusting the internal parameters, thereby overcoming the problems that the prior art has larger limitation on the spread spectrum code and is difficult to realize the non-rate characteristic, and leading the invention to have larger design space and higher decoding performance;
thirdly, the invention can use the same coder and decoder to realize different speed by cascading the fixed outer SC-RA coding and the adjustable inner repeated coding, thereby overcoming the problem of overhigh complexity of the prior art and realizing the reliable data transmission with low system complexity under different channel conditions and different user numbers.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is an encoding sub-flow diagram in the present invention;
FIG. 3 is a graph of simulation results of the present invention.
Detailed Description
Embodiments and effects of the present invention will be further described below with reference to the accompanying drawings.
Referring to fig. 1, the specific steps of this embodiment are as follows:
the method comprises the following steps: an initial sequence is generated.
Generating an initial sequence, u, for each of K users in an IDMA system s An initial sequence representing the s-th user;
step two: and carrying out non-rate code coding to obtain a coding sequence.
Referring to fig. 2, the specific implementation of this step is as follows:
(2.1) initial sequence u to s-th user s Carrying out outer SC-RA coding to obtain outer coder coding sequence
Figure BDA0002562180780000041
(2.1.1) initial sequence u of s-th user s Equally divided into L segmented sequences
Figure BDA0002562180780000042
i＝0,1,...,L-1；
(2.1.2) for each segmentation sequence
Figure BDA0002562180780000043
Respectively carries out the first rearrangement operation to obtain a rearrangement sequence->
Figure BDA0002562180780000044
(2.1.2a) sequencing of the fragments
Figure BDA0002562180780000045
M elements of (a;) do>
Figure BDA00025621807800000411
Sub-randomly arranged to obtain->
Figure BDA00025621807800000412
A new sequence->
Figure BDA0002562180780000046
Wherein->
Figure BDA00025621807800000413
Figure BDA00025621807800000414
Represents the largest integer not exceeding Q-1;
(2.1.2b) pairs of segmentation sequences u i The M elements in the list are randomly arranged for 1 time and taken as the front
Figure BDA00025621807800000415
Element to obtain a new sequence u i,q ,q＝Q-1；
(2.1.2c) combining the sequences obtained in the first two steps according to the sequence to obtain a rearranged sequence
Figure BDA0002562180780000047
Figure BDA0002562180780000048
(2.1.3) sequencing each segment
Figure BDA0002562180780000049
Is rearranged sub-sequence->
Figure BDA00025621807800000410
Respectively carrying out (i + q) times modulo-2 addition to obtain a combined sequence->
Figure BDA0002562180780000051
/>
Figure BDA0002562180780000052
Wherein the content of the first and second substances,
Figure BDA0002562180780000053
indicates the segmentation sequence->
Figure BDA0002562180780000054
The q-th rearranged subsequence of (1);
(2.1.4) pairs of combinatorial sequences
Figure BDA0002562180780000055
Performing accumulation operation to obtain coding sequence of outer encoder>
Figure BDA0002562180780000056
(2.1.4a) combining sequences
Figure BDA0002562180780000057
Is taken as the first element of the outer encoder coding sequence @>
Figure BDA0002562180780000058
(2.1.4b) combining sequences
Figure BDA0002562180780000059
The first two elements of (a) are modulo-2 added and taken as the second element of the outer encoder coding sequence->
Figure BDA00025621807800000510
(2.1.4c) combining sequences
Figure BDA00025621807800000511
In (1)The first three elements are summed modulo-2 and taken as the third element of the outer encoder coding sequence>
Figure BDA00025621807800000512
(2.1.4d) and so on to obtain the final coding sequence of the outer encoder
Figure BDA00025621807800000513
(2.2) outer encoder code sequence for s-th user
Figure BDA00025621807800000514
Coding the internal repeated codes to obtain the coding sequence c of the internal coder s ：
(2.2.1) to each of the segmentation sequences in (2.1.1)
Figure BDA00025621807800000515
Respectively carrying out second rearrangement operation to obtain a first sequence v s ：
(2.2.1a) segmented sequence
Figure BDA00025621807800000516
M elements of (a;) do>
Figure BDA00025621807800000524
Are arranged at random times to obtain->
Figure BDA00025621807800000525
In a new sequence>
Figure BDA00025621807800000517
Wherein->
Figure BDA00025621807800000526
Figure BDA00025621807800000527
Represents the largest integer not exceeding alpha-1;
(2.2.1b) segmentationSequence of
Figure BDA00025621807800000518
M elements of (4) are randomly arranged 1 time and the front of them is taken>
Figure BDA00025621807800000528
Element to obtain a new sequence->
Figure BDA00025621807800000519
m＝α-1；
(2.2.1c) the sequences of (2.2.1a) and (2.2.1b) are combined in order of succession to give a first sequence v s ：
Figure BDA00025621807800000520
Outer encoder code sequence in (2.2.2) pairs (2.1.4)
Figure BDA00025621807800000521
Is/are each/is>
Figure BDA00025621807800000522
Respectively carrying out rearrangement operation to obtain a second sequence p s ：
(2.2.2a) for each sequence
Figure BDA00025621807800000523
N elements of (a)>
Figure BDA00025621807800000529
Are arranged at random times to obtain->
Figure BDA00025621807800000530
A new sequence->
Figure BDA0002562180780000061
Wherein->
Figure BDA00025621807800000613
Figure BDA00025621807800000614
Represents the largest integer not exceeding β -1;
(2.2.2b) for each sequence
Figure BDA0002562180780000062
N elements are randomly arranged 1 times and the front of the N elements is taken>
Figure BDA00025621807800000615
Element to obtain a new sequence->
Figure BDA0002562180780000063
n＝β-1；
(2.2.2c) combining the sequences of (2.2.2a) and (2.2.2b) in sequence to obtain a second sequence v s ：
Figure BDA0002562180780000064
(2.2.3) first sequence v of (2.2.1) s And (2.2.2) a second sequence v s Merging according to the sequence to obtain the coding sequence c of the inner encoder s 。
Step 3, coding sequence c of inner coder of s-th user s Interweaving to obtain an interweaved sequence pi s ：
Figure BDA0002562180780000065
Wherein the content of the first and second substances,
Figure BDA0002562180780000066
indicates will->
Figure BDA0002562180780000067
Is randomly rearranged and/or is selected>
Figure BDA0002562180780000068
An mth subsequence representing the first sequence, m =0,1, ·, L-1; />
Figure BDA0002562180780000069
Indicates will->
Figure BDA00025621807800000610
Is randomly rearranged and/or is selected>
Figure BDA00025621807800000611
Denotes the nth subsequence of the second sequence, n =0,1.
Step 4, interleaving sequence pi s Binary phase shift keying BPSK modulation is carried out, the 01 sequence to be modulated is modulated into a +/-1 sequence, and a modulation sequence x is obtained s 。
Step 5, inputting the modulation sequence x of each user into a Gaussian multi-user channel to obtain an output sequence y:
Figure BDA00025621807800000612
wherein K represents the number of users, x s Denotes the modulation sequence of the s-th user, n denotes the variance σ 2 Gaussian noise sequence with mean 0.
And 6, decoding the output sequence y to obtain a decoded sequence.
The existing decoding methods include a multi-user detection joint iteration method, a serial interference elimination joint iteration method and a residual auxiliary multi-user detection joint iteration method. In this embodiment, but not limited to, a multi-user detection joint iteration method is adopted to decode the output sequence y, that is, the output sequence y is input to the basic signal estimator ESE and the K single-user posterior probability APP decoders, and a decoded sequence is obtained through multiple iterations.
The effects of the present invention can be further illustrated by the following simulations:
1. simulation experiment conditions are as follows:
simulation experiment software environment: visual Studio 2015.
The simulation experiment adopts a Gaussian multi-user channel model, the number of users is set to be 10, the sum rate is set to be 1.0, and the length of an initial sequence is 4800 bits.
2. Simulation content and simulation result analysis:
the encoding method of the present invention is used for encoding and decoding the initial sequence with similar length with the existing PR-SC-LDPC code and PCC code method, and the result is shown in FIG. 3.
In fig. 3, the ordinate represents the bit error rate and the abscissa represents the signal-to-noise ratio in dB. Wherein:
the solid line marked by the solid square represents a simulation result curve of coding and decoding the initial sequence with the length of 4894 bits by using the coding and decoding method of the invention;
the solid line marked by the solid circle represents a simulation result curve of coding and decoding the initial sequence with the length of 4854 bits by using the coding and decoding method of the conventional PR-SC-LDPC code;
the solid line marked by the solid triangle represents the simulation result curve of coding and decoding the initial sequence with the length of 4800 bits by using the coding and decoding method of the existing PCC code.
The dotted line represents the performance curve at the shannon limit.
As can be seen from FIG. 3, compared with the decoding result curve using the conventional PR-SC-LDPC and PCC, the decoding result curve using the method of the present invention has a significantly lower bit error rate using the coding and decoding scheme of the present invention at the same SNR.
It can also be seen from fig. 3 that the decoding result curve of the present invention is closer to the shannon limit curve, which shows that the present invention has higher decoding performance while reducing the system complexity.

Claims (3)

1. A rateless multi-user coding method for use in an interleaved multiple access IDMA system, comprising:
(1) Generating an initial sequence u for each user in the IDMA system;
(2) Carrying out outer SC-RA coding on the initial sequence u to obtain an outer coder coding sequence c j ：
(2a) Equally dividing the initial sequence u into L segmented sequences u i ,i＝0,1,...,L-1；
(2b) For each segmented sequence u i Performing a first rearrangement operation to obtain rearranged sequences
Figure FDA0004079688430000011
Figure FDA0004079688430000012
Wherein Q represents the number of subsequences of the rearranged sequence, u i,q Representing the ith sequence of segments u i Q =0,1, ·, Q-1;
said for each segmented sequence u i Respectively carrying out first rearrangement operation, and realizing the following steps:
(2b1) For the segmented sequence u i M elements of
Figure FDA0004079688430000017
Are arranged at random times to obtain->
Figure FDA0004079688430000018
A new sequence u i,q Wherein->
Figure FDA0004079688430000019
Figure FDA00040796884300000110
Represents the largest integer not exceeding Q-1;
(2b2) For the segmented sequence u i In the first place, M elements are randomly arranged 1 time and taken
Figure FDA0004079688430000016
Element to obtain a new sequence u i,q ,q＝Q-1；
(2b3) Combining the sequences obtained from (2 b 1) and (2 b 2) in sequence to obtain a rearranged sequence
Figure FDA0004079688430000013
Figure FDA0004079688430000014
(2c) Each segmentation sequence u i Rearranged subsequence u of i,q Respectively carrying out modulo-2 addition (i + q) times to obtain a combined sequence t j ：
Figure FDA0004079688430000015
Wherein u is j-q,q Representing a segmented sequence u j-q The q-th rearranged subsequence of (1);
(2d) For combined sequence t j Performing accumulation operation to obtain the coding sequence c of the outer encoder j ：
Figure FDA0004079688430000021
Wherein the content of the first and second substances,
Figure FDA0004079688430000022
representing outer encoder code sequences c j Q =0,1,.., L + Q-2;
the pair of combined sequences t j Performing accumulation operation, and realizing the following steps:
(2d1) Combining the sequences t j As the outer encoder code sequence c j First element of (1)
Figure FDA0004079688430000023
(2d2) Combining the sequences t j The first two elements of (a) are summed modulo-2 as the outer encoder code sequence c j Second element of (2)
Figure FDA0004079688430000024
(2d3) Combining the sequences t j The first three elements in the sequence are added modulo 2 to form the outer encoder code sequence c j Third element of (2)
Figure FDA0004079688430000025
(2d4) By parity of reasoning, the final outer encoder coding sequence is obtained
Figure FDA0004079688430000026
(3) Coding sequence c of external encoder j And (3) carrying out internal repeated code coding to obtain an internal coder coding sequence c:
(3a) Each of the segmentation sequences u of pair (2 a) i And respectively carrying out second rearrangement operation to obtain a first sequence:
Figure FDA0004079688430000027
/>
where α denotes each segment sequence u i The number of the sub-sequences of (a),
Figure FDA0004079688430000028
represents the mth subsequence of the first sequence, m =0,1, ·, L-1;
(3b) The outer encoder code sequence c of (2 d) j Each sequence of (1)
Figure FDA0004079688430000029
And (3) respectively carrying out rearrangement operation to obtain a second sequence:
Figure FDA00040796884300000210
wherein β represents each sequence
Figure FDA00040796884300000211
Number of sub-sequences of (4), based on the comparison result>
Figure FDA00040796884300000212
An nth subsequence representing a second sequence, n =0,1, ·, L + Q-2;
(3c) Combining the first sequence v in (3 a) and the second sequence p in (3 b) according to the sequence to obtain the coding sequence of the inner encoder
Figure FDA0004079688430000031
(4) Interweaving the coding sequence c of the inner encoder to obtain an interweaving sequence pi;
(5) Carrying out binary phase shift keying BPSK modulation on the interleaved sequence pi, and modulating a 01 sequence to be modulated into a +/-1 sequence to obtain a modulation sequence x;
(6) Inputting the modulation sequence x into a Gaussian multi-user channel to obtain an output sequence y;
(7) And decoding the output sequence y and outputting a decoded sequence.
2. The method of claim 1, wherein the interleaving sequence π obtained in (4) is represented as follows:
Figure FDA0004079688430000032
wherein, pi v m (v m ) Show that
Figure FDA0004079688430000033
Is randomly rearranged and/or is selected>
Figure FDA0004079688430000034
Represents the mth subsequence of the first sequence, m =0,1, ·, L-1; />
Figure FDA0004079688430000035
Indicates whether or not a combination>
Figure FDA0004079688430000036
Is randomly rearranged and/or is selected>
Figure FDA0004079688430000037
Denotes the nth subsequence of the second sequence, n =0,1.
3. The method of claim 1, wherein the output sequence y obtained in (6) is represented as follows:
Figure FDA0004079688430000038
where k represents the number of users, x k Denotes the modulation sequence of the k-th user, n denotes the variance σ 2 Gaussian noise sequence with mean 0.
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