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A Study on Low Complexity Decoding Algorithm of LDPC Codes

Yong Deng

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

In this paper,the decoding algorithm of low-density parity-check(LDPC)codes is analyzed,and a new decoding algorithm based on the belief propagation(BP)algorithm to eliminate the influence of cycles in the factor graph is proposed. In the traditional BP algorithm,the cycles of factor graph will send message back to its source,and this will decrease the decoding performance. The new algorithm records each cycle’s path and length of each node,and cuts off the path by which message is propagated when the message will come back. It can advance the decoding performance by protect the message of good quality be propagated as widely as possible. Our results of simulation show that the performance of new algorithm is not worse than that of traditional BP algorithm in the low SNR channel and the new algorithm significantly outperform traditional BP algorithm in good channel condition.

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In this paper,the decoding algorithm of low-density parity-check(LDPC)codes is analyzed,and a new decoding algorithm based on the belief propagation(BP)algorithm to eliminate the influence of cycles in the factor graph is proposed. In the traditional BP algorithm,the cycles of factor graph will send message back to its source,and this will decrease the decoding performance. The new algorithm records each cycle’s path and length of each node,and cuts off the path by which message is propagated when the message will come back. It can advance the decoding performance by protect the message of good quality be propagated as widely as possible. Our results of simulation show that the performance of new algorithm is not worse than that of traditional BP algorithm in the low SNR channel and the new algorithm significantly outperform traditional BP algorithm in good channel condition.
In this paper, the decoding algorithm of low-density parity-check (LDPC) codes is analyzed, and a new decoding algorithm based on the belief propagation (BP) algorithm to eliminate the influence of cycles in the factor graph is proposed. In the traditional BP algorithm, the cycles of factor graph sends message back to its source, and this decreases the decoding performance. The new algorithm records each cycle's path and length of each node, and cuts off the path by which message is propagated when the message comes back. It can advance the decoding performance by protect the message of good quality be propagated as widely as possible. Our results of simulation show that the performance of new algorithm is not worse than that of traditional BP algorithm in the low SNR channel and the new algorithm significantly outperform traditional BP algorithm in good channel condition.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.
To improve the performance of BP decoding for polar codes, researchers have developed a Belief Propagation List (BPL) decoding algorithm by executing multiple BP decoders in parallel.This algorithm outperforms traditional BP decoding based on single graph decoding, although it sacrifices some complexity and delay.Unlike this basic Polar-BPL decoding mentioned above, a low-density parity check like (LDPC-like) BPL decoding algorithm has been introduced into polar codes.This algorithm performs more efficient BP decoding iterations on sparse graphs.To further reduce the complexity and delay of LDPC-like BPL, and avoid analyzing all sparse graphs, this article proposes an improved LDPC-like BPL (ILDPC-like BPL) decoding algorithm based on selecting factor graphs.This algorithm analyzes differences in permuted factor graphs and selects these graphs with non-convergent decoding results to form a decoding list, allowing decoding to be completed with fewer graphs traversed and iterations, thereby reducing complexity and delay.On this basis, to improve the reliability of this algorithm, this article further adds a path metric (PM) mechanism, which can dynamically evaluate different sparse graphs' results in parallel decoding.The simulation results show that compared with LDPC-like BPL (random scheme), ILDPC-like BPL improves decoding performance while reducing decoding delay and complexity; Compared with basic Polar-BPL (cycle-shift scheme), this algorithm greatly reduces decoding delay and complexity while achieving similar performance.
In this paper, we improve performance of Low Density Parity Check (LDPC) codes by adding a large number of short cycles. Short cycles, especially cycles of length 4, degrade performance of LDPC codes if the standard BP (Belief Propagation) decoding is used. Therefore current researches have focused on removing cycles of length 4 for designing good performance LDPC codes. We found that a large number of cycles of length 4 improve performance of LDPC codes if a modified BP decoding is used. We present the modified BP decoding algorithm for LDPC codes with a large number of short cycles. We show that the modified BP decoding performance of LDPC codes with a large number of short cycles is better than the standard BP decoding performance of LDPC codes designed by avoiding short cycles.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm
Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.