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IEEE Communications Letters

A Unified Early Stopping Criterion for Binary and Nonbinary LDPC Codes Based on Check-Sum Variation Patterns

Guojun Han, Xingcheng Liu

Published Oct 19, 2010• 23 citations
Publisher

Abstract

In order to detect uncorrectable error frames and early terminate their iterative belief-propagation (BP) decoding for binary or nonbinary LDPC codes, a unified early stopping criterion using check-sum variation patterns is proposed. In addition to low computational overhead and easy choice of threshold parameters, it can be adapted to different channels. Simulation results show that the proposed criterion greatly reduces the average number of iterations (ANI) at low to medium signal-to-noise ratio (SNR) while keeping the error performance degradation negligible over a wide SNR region.

DOI
10.1109/lcomm.2010.100410.100998

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In order to detect uncorrectable error frames and early terminate their iterative belief-propagation (BP) decoding for binary or nonbinary LDPC codes, a unified early stopping criterion using check-sum variation patterns is proposed. In addition to low computational overhead and easy choice of threshold parameters, it can be adapted to different channels. Simulation results show that the proposed criterion greatly reduces the average number of iterations (ANI) at low to medium signal-to-noise ratio (SNR) while keeping the error performance degradation negligible over a wide SNR region.
The analog implementation of error control decoders is a competitive methodology compared with the digital implementation in power efficiency and throughput. In order to detect uncorrectable frames and early stop the iterative decoding of low-density parity check (LDPC) analog decoders, a probability stopping block using probabilities of satisfied checks is proposed. Simulation results show that the proposed criterion can greatly reduce the average number of iterations at low SNR, and has better tradeoff between complexity and performance than other stopping criteria using extrinsic information.
A weighted belief propagation decoding algorithm for low-density parity-check decoding is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. We propose an early stopping criterion which is based on the average weighted reliability measure of the hard output of decoder to detect undecodable blocks in an early stage of the decoding process. In addition, an adaptive weighted iteration scheme is proposed to increase the convergence speed of belief propagation (BP) decoding and therefore improve the error performance. The evolution of the adaptive weighting factor with the number of decoding iterations is based on the relative entropy between two consecutive ”a posteriori” probabilities distribution at decoder output. Simulation results show that the proposed algorithm can achieve about 0.2-0.4 dB coding gain improvement on average while reducing up to about 50%-85% iterations for decoding at low to medium E(subscript b)/ N(subscript 0) , compared with the conventional BP based algorithms.
Nonbinary low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, a new stopping criterion is proposed. Based on the changes of the variance of variable node¿s extrinsic information, the criterion can predict a decoding failure and decide whether the iteration of the decoder should be stopped. The simulation results show that the stopping criterion can greatly reduces the average number of required iterations of GF(q)-LDPC decoder with negligible performance loss.
The paper presents a novel approach to reduce the bit error rate (BER) in iterative belief propagation (BP) decoding of low density parity check (LDPC) codes. The behavior of the BP algorithm is first investigated as a function of number of decoder iterations, and it is shown that typical uncorrected error patterns can be classified into 3 categories: oscillating, nearly-constant, or random-like, with a predominance of oscillating patterns at high Signal-to-Noise (SNR) values. A proposed decoder modification is then introduced based on tracking the number of failed parity check equations in the intermediate decoding iterations, rather than relying on the final decoder output (after reaching the maximum number of iterations). Simulation results with a rate ¿ (1024,512) progressive edge-growth (PEG) LDPC code show that the proposed modification can decrease the BER by as much as 10-to-40%, particularly for high SNR values.
An efficient early stopping criterion based on the evolution of the number of reliable variable nodes (NRVN) is proposed for low density parity check (LDPC) codes in this paper. This criterion can significantly reduce the average number of iterations (ANI) at low to middle signal to noise ratios (SNRs) with minimal performance degradation. Furthermore, a hybrid decoding method is presented to reduce the decoding complexity of LDPC codes by combining the proposed stopping criterion and forced convergence (FC) decoding algorithm. Compared with the classic belief propagation (BP) decoding, significant computation complexity reduction can be achieved with small computation overhead.
A properly designed stopping criterion for iterative decoding algorithms can save a number of iterations and lead to a considerable reduction of system latency. The symbol flipping decoding algorithms based on prediction (SFDP) have been proposed recently for efficient decoding of non-binary low-density parity-check (LDPC) codes. To detect the decoding frames with slow convergence or even non-convergence, we track the number of oscillations on the value of objective function during the iterations. Based on this tracking number, we design a simple stopping criterion for the SFDP algorithms. Simulation results show that the proposed stopping criterion can significantly reduce the number of iterations at low signal-to-noise ratio regions with slight error performance degradation.