CN113114269A - Belief propagation-information correction decoding method - Google Patents

Belief propagation-information correction decoding method Download PDF

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CN113114269A
CN113114269A CN202110409976.4A CN202110409976A CN113114269A CN 113114269 A CN113114269 A CN 113114269A CN 202110409976 A CN202110409976 A CN 202110409976A CN 113114269 A CN113114269 A CN 113114269A
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邢莉娟
李卓
韩晓昳
张萌
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Xidian University
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Abstract

A belief propagation-information correction decoding method comprises the following steps: and in the original belief propagation BP decoding, Cyclic Redundancy Check (CRC) is adopted as a check code for early termination of iteration, if the CRC does not pass after the maximum iteration times, a point in a set selected by using a minimum log-likelihood ratio method is corrected, and then iteration is continued until the CRC passes. The method greatly improves the decoding performance under the condition of losing a certain complexity, and has the same complexity as the original BP under the condition of high signal-to-noise ratio, so that the polarization code based on belief propagation-information correction decoding is used in deep space communication.

Description

Belief propagation-information correction decoding method
Technical Field
The disclosure belongs to the technical field of communication, and particularly relates to an improved method of a polarization code based on a belief propagation decoding algorithm.
Background
Cosmic communication is called space communication and deep space communication, wherein deep space communication is aimed at leaving the earth's surface by more than 2 x 106Kilometer space, which is the communication between earth stations and detectors in this distance into the solar system, is an essential component of deep space exploration technology. The channel transmission under deep space communication has the characteristics of long communication distance, large path loss, high working frequency and the like, and has high work receiving capacityThe influence of interference factors such as rate limit, transmission delay, cosmic rays and the like requires low power consumption, small volume and light weight of related devices, and also requires an extremely low bit error rate under a low signal-to-noise ratio, and in order to improve the receiving sensitivity and channel gain of a system and enhance the receiving capability of weak signals, a main measure is to adopt a channel coding technology. Since deep space communication is rich in bandwidth resources, a channel coding scheme with low bandwidth utilization efficiency can be used. The channel coding technology can provide considerable coding gain, resist communication path loss caused by long distance and improve communication reliability; meanwhile, the system power can be greatly reduced by improving the coding gain.
In the early stage of development of deep space communication coding technology, the most widely used channel coding is a serial concatenated code in which a convolutional code is used as an inner code and an RS code is used as an outer code. The convolutional code is simple to realize, the decoding threshold is low, the decoding complexity of the RS code is low, and high coding gain can be obtained when the error rate of input information is high. Since the last 90 s, the discovery and important development of Turbo codes and LDPC codes have greatly promoted the development of channel coding technology, so that the actual channel coding performance is closer to the Shannon limit, and the Turbo codes and LDPC codes can be quickly applied to occasions such as ground mobile communication and the like along with the popularization of the application. In 1999, the spatial Data System council (CCSDS, coherent Committee for Space Data System) added Turbo codes to the telemetry channel coding recommendation as a channel coding standard for satellite communication and deep Space communication. In 2007, the LDPC code has low implementation complexity due to its high coding gain, and good parallel decoding performance is also listed in the deep space channel coding and decoding standard by CCSDS. The polarization code is the first error correcting code which can reach the Shannon capacity theoretically, and the low complexity of coding and decoding enables the polarization code to have huge application potential. The polarization code is used as a coding and decoding scheme of a deep space communication channel, so that the communication quality can be effectively improved.
Disclosure of Invention
In order to solve the above problem, the present disclosure provides a belief propagation-information correction decoding method, including the following steps:
and in the original belief propagation BP decoding, Cyclic Redundancy Check (CRC) is adopted as a check code for early termination of iteration, if the CRC does not pass after the maximum iteration times, a point in a set selected by using a minimum log-likelihood ratio method is corrected, and then iteration is continued until the CRC passes.
The scheme adopts a Belief Propagation-Information Correction (BP-IC) decoding algorithm to greatly improve the decoding performance under the condition of losing certain complexity, and has the same complexity with the original BP under the condition of high signal-to-noise ratio, compared with the original BP decoding, the performance gain of 0.8dB is realized, and the complexity loss can be ignored under the condition of high signal-to-noise ratio. Compared with other improved algorithms, the method has better performance and lower complexity under the condition of low signal-to-noise ratio, and is suitable for the characteristic of low signal-to-noise ratio in deep space communication. In addition, due to the inherent parallelism of BP decoding, the time delay of the BP decoding is lower than that of SCL series decoding, so that the selection of the AWGN channel in the coherent time to simulate deep space communication is more feasible.
Drawings
FIG. 1 is a flow chart of a belief propagation-information correction decoding method provided in one embodiment of the present disclosure;
FIG. 2 is a comparison graph of bit error rates at different signal-to-noise ratios (SNRs) for three decoding algorithms provided in one embodiment of the present disclosure;
fig. 3 is a comparison graph of average iteration numbers under three decoding algorithms provided in an embodiment of the present disclosure.
Detailed Description
In one embodiment, the present disclosure provides a belief propagation-information correction decoding method, including the steps of:
and in the original belief propagation BP decoding, Cyclic Redundancy Check (CRC) is adopted as a check code for early termination of iteration, if the CRC does not pass after the maximum iteration times, a point in a set selected by using a minimum log-likelihood ratio method is corrected, and then iteration is continued until the CRC passes.
According to the scheme, CRC is adopted as a check code for early termination of iteration, so that the average iteration number of BP decoding is reduced, and further, the average iteration number of BP decoding is reducedThe decoding time delay and complexity are reduced; on the basis of original BP decoding, information correction and additional iteration operation are added, the BP decoding performance is greatly improved under the condition of losing a certain complexity, and the complexity similar to that of the original BP decoding is achieved under the condition of high signal-to-noise ratio. Reception information considering channel
Figure BDA0003022076910000031
If the received information y of a certain pointiUnreliable, and decoding failure may occur through iteration. It is found experimentally that by counting a point y in the received informationiCorrecting the information to obtain LLR (y)i) The modification is + ∞ and- ∞, and the decoding can be modified by continuous iteration, so that the decoding performance is improved. To point yiThe selection of (a) adopts a minLLR scheme, and T | LLRs (y) are selectedi) The smallest point component set
Figure BDA00030220769100000411
A correction attempt is made for each point in turn.
In another embodiment, the definition of some variables in the polar code encoding is as follows:
w: a binary input memoryless channel with one input u e {0, 1} and an output y e y is represented.
N: code length of polarization code: n is 2n。
K: the polarization code information bit length is K.
GN: is an invertible generator matrix of size N x N. Wherein
Figure BDA0003022076910000041
Figure BDA0003022076910000042
Figure BDA0003022076910000043
Expressed as the n-dimensional kronecker product of a matrix.
Figure BDA0003022076910000044
Bit vectors before encoding.
Figure BDA0003022076910000045
The encoded output bit vector.
Figure BDA0003022076910000046
Is the received vector of the decoder.
W(yi|xi): corresponding to the channel transition probability of each bit.
In the above definition of variables, the encoding operation of the polar code is performed, i.e.
Figure BDA0003022076910000047
After channel combination in the channel polarization process, a synthetic vector channel is obtained
Figure BDA0003022076910000048
Polarising the sub-channels after channel separation
Figure BDA0003022076910000049
Is defined as
Figure BDA00030220769100000410
Wherein
Figure BDA0003022076910000051
Figure BDA0003022076910000052
Is that
Figure BDA0003022076910000053
The sub-vectors of (2).
In all polarized channels
Figure BDA0003022076910000054
In the method, K most reliable sub-channels are selected, and the corresponding position indexes form a set
Figure BDA0003022076910000055
Is called information set and
Figure BDA0003022076910000056
set of position indices of remaining unreliable sub-channels
Figure BDA0003022076910000057
Called frozen set. Freezing collections
Figure BDA0003022076910000058
The method is characterized in that both the transmitting end and the receiving end are known, when the transmitting end transmits information and the receiving end recovers the information, the value of the corresponding position of an element in a freezing set is set as a fixed value, and the value of a freezing bit is set to be 0 in the method.
In another embodiment, the BP decoding of the polar code is directed to receiving information
Figure BDA0003022076910000059
And information collection
Figure BDA00030220769100000510
Obtaining a source bit sequence
Figure BDA00030220769100000511
BP decoding is a parallel decoding algorithm, has the characteristics of low decoding time delay, high throughput rate and the like, and is easy to realize by hardware. In the Tanner graph of the polar code generator matrix, each point contains information R [ i ] from left to right][j]And information L [ i ] from right to left][j]Wherein: i is more than or equal to 0 and less than N, and j is more than or equal to 1 and less than or equal to N + 1. And transmitting the information left and right, iterating until the maximum iteration times is reached or a preset stop condition is met, ending the decoding, and outputting a decoding result. The decoding is specifically described by the following algorithm:
inputting: is connected withReceive vector
Figure BDA00030220769100000512
Transition probability LLR (y) for each pointi)；
Initialization: initializing L [ i ] [ j ] and R [ i ] [ j ] in the Tanner graph, updating the information of the leftmost end and the rightmost end in the graph according to the following formula, and initializing the information of other points to be 0;
Figure BDA00030220769100000513
L[i][n+1]＝LLR[yi]
iteration: and performing iteration from right to left and then from left to right in each processing unit according to the following iteration formula until a preset maximum iteration frequency is reached or a preset iteration stopping condition is met.
L[i][j]＝g(L[2i-1][j+1]，L[2i][j+1]+R[i+N/2j][j])
L[i+N/2j][j]＝g(R[i][j]，L[2i-1][j+1])+L[2i][j+1]
R[2i-1][j+1]＝g(R[i][j]，L[2i][j+1]+R[i+N/2j][j])
R[2i][j+1]＝g(R[i][j]，L[2i-1][j+1])+R[i+N/2j][j]
Wherein:
Figure BDA0003022076910000061
and (3) outputting: and (3) judging according to the value of L [ i ] [1] at the end of iteration:
Figure BDA0003022076910000062
in another embodiment, referring to FIG. 1, the BP-IC decoding specific algorithm steps are as follows:
s100: using received vectors of a decoder
Figure BDA0003022076910000063
Log likelihood ratio LLR (y)i) Initialization of L [ i ]][n+1]Using sets of information
Figure BDA0003022076910000064
Initialization of R [ i ]][1](ii) a Wherein R [ i ]][j]Indicating information from left to right, L [ i ]][j]Representing information from right to left, i represents the ith node, j represents the jth layer of the Tanner graph, i is more than or equal to 0 and less than N, j is more than or equal to 1 and less than or equal to N +1, and N is an integer;
s200: carrying out original BP decoding iteration, using CRC as check code for early termination of iteration, if passing CRC, ending decoding, and outputting decoding result
Figure BDA0003022076910000065
Otherwise, continuing the iteration until reaching the preset maximum iteration times;
s300: if the original BP decoding fails, the information correction operation is carried out: storing information of each point L and R in a Tanner graph under the current state by using L 'and R'; ② due to L [ i ]][n+1]The information is determined by the channel output and remains unchanged in the iteration, for LLR (y), because it is located in the rightmost layer of the Tanner graphi) Sorting the absolute values of the points, and selecting the T points with the minimum absolute value, namely:
Figure BDA0003022076910000066
recording point collection
Figure BDA0003022076910000071
S400: to the point set
Figure BDA0003022076910000072
The points are corrected one by one;
s500: when the previous correction cannot realize correct decoding, the stored information of L 'and R' is used for refreshing the Tanner graph in the current state, so that error propagation in the Tanner graph caused by error correction is avoided; if the correct decoding is not carried out after the correction of the j point, continuing to carry out the correction of the j +1 point, and repeating the S400 until the point correction of the whole set is finished;
s600: if the CRC check is not passed after the correction operation is finished, outputting the final data
Figure BDA0003022076910000073
As a result of the decoding.
For the embodiment, the BP-IC decoding based on the minLLR selection strategy has good performance which can be compared with the CA-SCL decoding, and the average complexity and the time delay are close to the original BP decoding under the higher signal-to-noise ratio. And compared with a similar BPF algorithm (a certain point in a reverse decoding result), the BP-IC decoding has lower decoding complexity under the condition of reaching the same error rate.
And storing the information of each point L and R in the Tanner graph in the current state by using L '[ i ] [ j ] and R' [ i ] [ j ]. The polar code BP decoding is an iterative decoding of a Tanner graph based on a polar code generator matrix. The Tanner graph in the current state is a BP decoding basic operation unit graph.
In another embodiment, step S400 further comprises: selected point ijTo L [ i ]j][n+1]Sequentially modifying the parameters to be + ∞ and- ∞, continuing to perform additional iteration on the basis, ending decoding after each iteration through CRC, and otherwise, continuing to iterate until the maximum iteration number is reached;
in another embodiment, polarization codes based on belief propagation-information correction decoding are applied to deep space communication.
In another embodiment, the channel for deep space communication is modeled as a generic AWGN channel, and a Monte Carlo method is used to integrate information using a polar code in deep space communication under the AWGN channel
Figure BDA0003022076910000081
The construction is carried out.
For this embodiment, the free space segment of the deep space communication channel can be approximated as an ideal memoryless white gaussian noise channel, with the noise characteristics in the received signal resembling additive white gaussian noise. And because of the inherent parallel characteristic of BP-based decoding, compared with SC series decoding, the decoding time delayAnd even more, multipath and other factors can not be considered in the coherent time, so that the channel of deep space communication is simulated into an AWGN channel with constant parameters, and the information set is constructed by using Monte Carlo
Figure BDA0003022076910000082
When constructing Polar codes, the input of the algorithm is three parameters, namely (W, N, K), wherein W is used for polarized channels, N is the code length of the Polar codes, and K is the number of information bits of the Polar codes. The algorithm finally generates a K-dimensional information set
Figure BDA0003022076910000083
It makes it possible to
Figure BDA0003022076910000084
The smaller the value of (A), the better. Therefore, only calculate all the parameters
Figure BDA0003022076910000085
And sorting them, the problem of code construction can be solved. However, the complexity of constructing the polarization code to be precise is too high, and parameters can be estimated
Figure BDA0003022076910000086
The method of (2) to approximately construct a polarization code. Wherein:
Figure BDA0003022076910000087
in another embodiment, the specific implementation steps of the configuration are as follows:
s1: generating a set of random sequences
Figure BDA0003022076910000088
Figure BDA0003022076910000089
The number of the middle element is the code length N of the constructed polarization code;
S2: to the sequence
Figure BDA0003022076910000091
Performing polarization coding to generate information sequence
Figure BDA0003022076910000092
S3: pair after coding
Figure BDA0003022076910000093
BPSK modulation is carried out to the information sequence
Figure BDA0003022076910000094
Conversion into modulated sequences
Figure BDA0003022076910000095
S4: modulating the obtained modulation sequence
Figure BDA0003022076910000096
With AWGN channels, the result is obeyed to a mean of 0 and a variance of
Figure BDA0003022076910000097
Normally distributed noise, channel reception sequence
Figure BDA0003022076910000098
S5: obtaining a transition probability W (y) of a channeli|xi)；
S6: SC decoding is performed, the input is W (y)i|xi) The output is the probability of calculating the polarized sub-channel of each point
Figure BDA0003022076910000099
Wherein u isiFor a channel
Figure BDA00030220769100000910
The input bits of (a) are selected,
Figure BDA00030220769100000911
is a channel
Figure BDA00030220769100000912
The output bit of (1);
s7: calculating parameters:
Figure BDA00030220769100000913
s8: repeating the steps S1-S7, calculating the average value of the parameters as each point
Figure BDA00030220769100000914
Then sorted in descending order and then the position of the frozen bit is selected.
For this embodiment, if the code rate of the constructed codeword is R, then
Figure BDA00030220769100000915
Select the first NR larger
Figure BDA00030220769100000916
The corresponding index position is the position of the frozen bit. Step S6 indicates when we have obtained the received bit data
Figure BDA00030220769100000917
And the results of the (i-1) decoding outputs are obtained, we can apply the formula
Figure BDA00030220769100000918
Calculated transition probability of each sub-channel after channel splitting, i.e.
Figure BDA0003022076910000101
Information sequence
Figure BDA0003022076910000102
Is a vector of encoded output bits, i.e.
Figure BDA0003022076910000103
The encoded output bit vector.
In another embodiment, the step S2 further includes:
Figure BDA0003022076910000104
wherein G isNIs an invertible generator matrix of size N x N.
In another embodiment, the step S5 further includes: calculating channel transition probability
Figure BDA0003022076910000105
Where σ represents the standard deviation of the gaussian distribution to which the probability density function of the noise obeys.
In another embodiment, the simulation experiment uses Binary Phase Shift Keying (BPSK), and in the simulated AWGN deep space communication channel, the code length is selected to be 2048, the code rate is 0.5, and the CRC with the length of 24 is selected as the error detection code.
Fig. 2 shows the performance comparison of the polar code with code length N of 2048 and code rate of 0.5 under three decoding algorithms, where T of BP-IC is 16 and T of BP-IC is 64, and CRC is 24. FIG. 2 compares the bit error rates of BP-IC decoding algorithm at different signal-to-noise ratios (SNR), and selects the set sizes respectively
Figure BDA0003022076910000106
16 and 64 respectively, and compared with the original BP decoding and belief propagation bit reversal decoding (BPF) which take CRC as an early termination condition, the simulation shows that the BP-IC decoding based on the minLLR selection strategy has good performance, and the error rate is 10-3There is a gain of 0.8dB and performance is better than BPF decoding at low signal-to-noise ratios.
In another embodiment, fig. 3 compares the delay and complexity of several decoding operations, and the statistical average number of iterations is used as the criterion for decoding delay and complexity, and the less the number of iterations, the lower the complexity and delay. It is known from the figure that the average number of iterations approaches the original BP decoding at higher signal-to-noise ratios. And compared with a similar BPF algorithm, the complexity of the two algorithms is similar, but the decoding complexity of BP-IC decoding is lower under a low signal-to-noise ratio.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (8)

1. A belief propagation-information correction decoding method comprises the following steps:
and in the original belief propagation BP decoding, Cyclic Redundancy Check (CRC) is adopted as a check code for early termination of iteration, if the CRC does not pass after the maximum iteration times, a point in a set selected by using a minimum log-likelihood ratio method is corrected, and then iteration is continued until the CRC passes.
2. The method according to claim 1, preferably, the method is specifically:
s100: using received vectors of a decoder
Figure FDA0003022076900000011
Log likelihood ratio LLR (y)i) Initialization of L [ i ]][n+1]Using sets of information
Figure FDA0003022076900000015
Initialization of R [ i ]][1](ii) a Wherein R [ i ]][j]Indicating information from left to right, L [ i ]][j]Representing information from right to left, i represents the ith node, j represents the jth layer of the Tanner graph, i is more than or equal to 0 and less than N, j is more than or equal to 1 and less than or equal to N +1, and N is an integer;
s200: performing original BP decoding iteration, using CRC as the correction for early termination of iterationChecking the code, if passing CRC, ending decoding, outputting the decoding result
Figure FDA0003022076900000012
Otherwise, continuing the iteration until reaching the preset maximum iteration times;
s300: if the original BP decoding fails, the information correction operation is carried out: storing information of each point L and R in a Tanner graph under the current state by using L 'and R'; ② due to L [ i ]][n+1]The information is determined by the channel output and remains unchanged in the iteration, for LLR (y) because it is located at the rightmost layer of the polar code decoded Tanner graphi) Sorting the absolute values of the points, and selecting the T points with the minimum absolute value, namely:
Figure FDA0003022076900000013
recording point collection
Figure FDA0003022076900000014
S400: to the point set
Figure FDA0003022076900000016
The points are corrected one by one;
s500: when the previous correction cannot realize correct decoding, the stored information of L 'and R' is used for refreshing the Tanner graph in the current state, so that error propagation in the Tanner graph caused by error correction is avoided; if the correct decoding is not carried out after the correction of the j point, continuing to carry out the correction of the j +1 point, and repeating the S400 until the point correction of the whole set is finished;
s600: if the CRC check is not passed after the correction operation is finished, outputting the final data
Figure FDA0003022076900000021
As a result of the decoding.
3. The method of claim 2, step S400 further comprisingThe method comprises the following steps: selected point ijTo L [ i ]j][n+1]And sequentially modifying the parameters to be + ∞ and- ∞, continuing to perform additional iteration on the basis, ending decoding after each iteration is performed through CRC, and otherwise, continuing to perform iteration until the maximum iteration number is reached.
4. The method of claim 1, applying belief propagation-information based revision decoded polarization codes to deep space communications.
5. The method of claim 4, modeling the channel for deep space communication as a generic AWGN channel, using a Monte Carlo method for information sets using polar codes in deep space communication under AWGN channel
Figure FDA00030220769000000211
The construction is carried out.
6. The method of claim 5, wherein the specific implementation steps of the configuration are as follows:
s1: generating a set of random sequences
Figure FDA0003022076900000022
The number of the middle element is the code length N of the constructed polarization code;
s2: to the sequence
Figure FDA0003022076900000023
Performing polarization coding to generate information sequence
Figure FDA0003022076900000024
S3: pair after coding
Figure FDA0003022076900000025
BPSK modulation is carried out to the information sequence
Figure FDA0003022076900000026
Transformation ofFor modulating the sequence
Figure FDA0003022076900000027
S4: modulating the obtained modulation sequence
Figure FDA0003022076900000028
With AWGN channels, the result is obeyed to a mean of 0 and a variance of
Figure FDA0003022076900000029
Normally distributed noise, channel reception sequence
Figure FDA00030220769000000210
S5: obtaining a transition probability W (y) of a channeli|xi)；
S6: SC decoding is performed, the input is W (y)i|xi) The output is the probability of calculating the polarized sub-channel of each point
Figure FDA0003022076900000031
Wherein u isiFor a channel
Figure FDA0003022076900000032
The input bits of (a) are selected,
Figure FDA0003022076900000033
is a channel
Figure FDA0003022076900000034
The output bit of (1);
s7: calculating parameters:
Figure FDA0003022076900000035
s8: repeating the steps S1-S7, calculating the average value of the parameters as each point
Figure FDA0003022076900000036
Then sorted in descending order and then the position of the frozen bit is selected.
7. The method of claim 6, wherein the step S2 further comprises:
Figure FDA0003022076900000037
wherein G isNIs an invertible generator matrix of size N x N.
8. The method of claim 6, wherein the step S5 further comprises: calculating channel transition probability
Figure FDA0003022076900000038
Where σ represents the standard deviation of the gaussian distribution to which the probability density function of the noise obeys.
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Publication number Priority date Publication date Assignee Title
CN113572577A (en) * 2021-07-28 2021-10-29 北京邮电大学 Novel method and system for shortening polarization code
CN113572577B (en) * 2021-07-28 2022-04-26 北京邮电大学 Novel method and system for shortening polarization code
CN114422084A (en) * 2022-01-18 2022-04-29 重庆邮电大学 AD-SCL decoding method based on high-low LLR (ratio of likelihood to variance) ratio
CN114422084B (en) * 2022-01-18 2024-03-26 重庆邮电大学 AD-SCL decoding method based on high-low LLR duty ratio

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