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Journal of Xidian University

A fast convergence decoding algorithm for LDPC codes

Xinmei Wang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

A realization of belief propagation algorithms based on the two-way schedule and a serial concatenated decoding algorithm for LDPC codes based on the matrix decomposition are presented. The performance of this new algorithm is systematically analyzed via the density evolution theory. Analysis and simulation results show that the serial concatenated decoding algorithm demonstrates a higher convergence speed and has as good performance as the conventional belief propagation algorithm.

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A realization of belief propagation algorithms based on the two-way schedule and a serial concatenated decoding algorithm for LDPC codes based on the matrix decomposition are presented. The performance of this new algorithm is systematically analyzed via the density evolution theory. Analysis and simulation results show that the serial concatenated decoding algorithm demonstrates a higher convergence speed and has as good performance as the conventional belief propagation algorithm.
We propose a new belief propagation (BP) decoding algorithm for fast convergence decoding of regular LDPC codes. The fast convergence is achieved by grouping and scheduling updates of nodes on a bipartite-graph without additional computations or approximations. For this reason, the proposed algorithm can be applied to a serially constructed decoder, and can reduce the power consumption and decoding delay of the decoder. Simulation results show that the convergence speed of the proposed algorithm depends on the degree, d/sub v/, of the variable-nodes of the bipartite-graph, and the average number of iterations of the decoder can be reduced to (d/sub v/-1)/d/sub v/ by using the proposed algorithm without performance degradation or additional computation.
Serial decoding schedules for low-density parity-check (LDPC) codes are described and analyzed. Conventionally, in each iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (“flooding schedule”). In contrast, in the considered methods, the updating of the nodes is implemented according to a serial schedule. The evolution of the decoding algorithm’s computation tree under serial scheduling is analyzed. The analysis shows that it grows twice as fast in comparison to the flooding schedule’s computation tree, indicating that the serial schedule propagates information twice as fast in the code’s underlying graph. Furthermore, asymptotic analysis of the serial schedule’s convergence rate is done using the Density Evolution (DE) algorithm. Applied to various ensembles of LDPC codes, it shows that when working near the ensemble’s threshold, for long enough codes the serial schedule is expected to converge in half the number of iterations compared to the standard flooding schedule. This observation is generally proved for the Binary Erasure Channel (BEC) under some likely assumptions. Finally, an accompanying concentration theorem is proved, justifying the asymptotic DE analysis assumptions. 1
Formulas for updated rules of the belief propagation algorithm applied to low density parity check (LDPC) codes are systematically derived based on the tree and the finite state machine (FSM).The probability measure on the continuous message space is introduced to evaluate the evolution of message densities within iterative decoding rounds,and derivations of the output distributions of common binary symmetric channels and the message density evolution are given in detail.The parameterized estimation of the performance of the algorithm is also discussed.The analytic and calculable means can be used to make systematical analysis for the convergence of BP algorithms independent of channels,and can be of help in designing LDPC codes and analyzing quantization effects for the fast decoding on the purpose of practical applications of LDPC codes to real time communication systems.