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International Conference on Communications

Two decoding algorithms for low-density parity-check codes

Telex M. N. Ngatched, Martin Bossert, A. Fahrner

Published Aug 16, 2005• 3 citations
Publisher

Abstract

In this paper, a low complexity algorithm for binary linear block codes is applied to low-density parity-check (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performance at smaller complexity.

DOI
10.1109/icc.2005.1494436

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In this paper, a low complexity algorithm for binary linear block codes is applied to low-density parity-check (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performance at smaller complexity.
In this letter, a low complexity decoding algorithm for binary linear block codes is applied to low-density paritycheck (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity.
In this paper, we introduce a new bit-flipping decoding algorithm for low-density parity-check codes based on loop detection mechanism, which is an extension to soft-decision decoding. This decoding algorithm's performance has been significantly improved by introducing a loop detection mechanism for the failed flipping bit and leading into the soft-decision about the reliability measure of the received symbols. Theoretical analysis shows that the complexity of this algorithm is lower. Some simulation results are given, which show that compared with other known kinds of bit-flipping decoding algorithms for LDPC codes, this new decoding on the additive white Gaussian noise channel offer excellent performance.
An improved bit-flipping decoding algorithm is proposed for low-density parity-check(LDPC) codes in this paper.Two influences on error probabilities of code bits are considered: the influence of the number of code bits included in an unsatisfied check,and the influence of the number of unsatisfied checks of each code bit.No soft information is required for decoding.Simulation results show that improvement on performance is observed for the proposed algorithm,and it provides better performance over several soft-decision bit-flipping decoding algorithms for LDPC codes with large girth.
An improved bit-flipping(BF) algorithm with low complexity for decoding structured low-density parity-check codes(LDPC) is proposed to improve the performance of the hard-decision BF algorithm.The hard-decision bits are divided into two groups based on the magnitudes of the received symbols,and at each iteration,the proposed algorithm can flip more than one bit with using two thresholds,and the flipping error probability is effectively decreased.The improved BF algorithm requires some real number comparisons before iterations and requires only logical operations during the iterations.Compared with the weighted bit-flipping algorithm and its modifications,the new method is with significantly lower complexity.Simulations show that the proposed algorithm is provided with very fast convergence speed and excellent performance with significantly low complexity.
Recent advances in coding theory have uncovered the previously forgotten power of Low-Density Parity-Check (LDPC) codes. Their popularity can be related to their relatively simple iterative decoders and their potential to achieve high performance close to shannon limit. These make them an attractive candidate for error correcting application in communication systems. In this thesis, we focus our research on the iterative decoding algorithms for Low-Density Parity-Check codes and present an improved decoding algorithm. First, the graph structure of LDPC codes is studied and a graph-based search algorithm to find the shortest closed walk and shortest cycle for each node of the graph is proposed. Then, the Deterministic schedule is applied on nodes of the graph with the objective of preserving the optimality of the algorithms. Finally, Hybrid Switch-Type technique is applied on the improved algorithms to provide a desirable complexity/performance trade-off. Hybrid Technique and Deterministic schedule are combined for decoding regular and irregular LDPC codes. The performance and complexity of the decoder is studied for Sum-Product and Gallager A algorithms. The result is a flexible decoder for any available LDPC code and any combination of decoding algorithms based on the communication systems need. In this technique, we benefit the high performance of soft-decision algorithms and low complexity of hard-decision algorithms by changing the decoding rule after a few iterations. Hence, a desirable performance can be obtained with less average number of soft iterations. Moreover, all the nodes do not update messages in each iteration. As a result, the total number of computations is reduced considerably
Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic decoding algorithms are attractive for nonbinary LDPC codes, since they involve only finite field additions and multiplications as well as integer operations and, hence, have significantly lower complexity than other algorithms. In this paper, we propose two improvements to the majority-logic decoding algorithms. Instead of the accumulation of reliability information in the existing majority-logic decoding algorithms, our first improvement is a new reliability information update. The new update not only results in better error performance and fewer iterations on average, but also further reduces computational complexity. Since existing majority-logic decoding algorithms tend to have a high error floor for codes whose parity check matrices have low column weights, our second improvement is a reselection scheme, which leads to much lower error floors, at the expense of more finite field operations and integer operations, by identifying periodic points, reselecting intermediate hard decisions, and changing reliability information.