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An Adaptive Algorithm and Stopping Criterion for LDPC Decoding

Tso-Cho Chen

Published Jul 1, 2011• 0 citations
Publisher

Abstract

A new adaptive and early stopping scheme for low-density parity-check (LDPC) decoding is proposed for accelerating the convergence of message-passing algorithms. The new algorithm is based on the cross-entropy between two consecutive a posteriori probabilities distribution of the soft output of decoder. Information-theoretic support and extensive simulations are provided to demonstrate the efficiency of the proposed adaptive algorithm and early stopping criterion. The proposed scheme can significantly reduce the average number of iterations of decoder while having a comparable or even better performance than conventional message-passing algorithms.

DOI
10.7095/jcust.201107.0101

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A new adaptive and early stopping scheme for low-density parity-check (LDPC) decoding is proposed for accelerating the convergence of message-passing algorithms. The new algorithm is based on the cross-entropy between two consecutive a posteriori probabilities distribution of the soft output of decoder. Information-theoretic support and extensive simulations are provided to demonstrate the efficiency of the proposed adaptive algorithm and early stopping criterion. The proposed scheme can significantly reduce the average number of iterations of decoder while having a comparable or even better performance than conventional message-passing algorithms.
An adaptive decoding scheme for low-density parity-check (LDPC) codes is proposed for accelerating the convergence of message-passing algorithms. The evolution of adaptive weighting factor with the number of decoding iterations and stopping criterion are based on the cross-entropy between two consecutive a posteriori probabilities distribution of the soft output of decoder. Information-theoretic support and extensive simulations are provided to demonstrate the efficiency of the proposed algorithm for LDPC decoding. The proposed adaptive decoding algorithm can reduce significantly the average number of iterations of decoder while having a comparable or even better performance than conventional message-passing algorithms.
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.
Nonbiliary low-density parity-check (LDPC) codes can lead to excellent error performance while the codewords are of short or moderate length. However, the high decoding complexity of nonbiliary LDPC codes inevitably depreciates their practical values. The computational bottleneck arises from the check node processing in the iterative message passing (MP) algorithms which terminate when either all parity checks are satisfied or the maximum iteration number is reached. We have observed that for undecodable blocks, the MP algorithms always run up to the maximum iteration limit and therefore cannot generate the correct codeword. Thus, it would be better to terminate the algorithms early so as to save the unnecessary computational time and reduce the extra power consumption when undecodable blocks are experienced. In this paper, we propose a new T-tolerance stopping criterion for LDPC decoders by exploiting the fact that the total a posteriori probability (APP) should increase as the iteration number grows. Simulation results demonstrate that our proposed new T-tolerance criterion can greatly reduce the average iteration number (complexity) while restricting the decoding performance degradation within 0.1 dB in low bit-energy-to-noise ratio scenarios.
Low density parity check (LDPC) codes are amongst the most powerful codes known today. They are decoded iteratively by a message-passing algorithm. For this, an inherent stopping criterion exists for decodable blocks based on parity checks. For undecodable blocks, typically, a fixed number of iterations are carried out before the decoding procedure is terminated, which is a waste of energy and time. We present a stopping criterion which detects undecodable blocks in an early stage of the decoding process. The novel stopping criterion works for floating and fixed point implementations. It greatly reduces the average number of required iterations without any loss in communication performance.
Low-density parity-check (LDPC) codes are favorable in low bit-error-rate and high code-rate applications. However, the decoding complexity for LDPC codes is quite large, especially for nonbinary LDPC codes. In this paper, we propose a new T-tolerance stopping criterion for LDPC decoders by exploiting the fact that the total aposteriori probability (APP) should increase across iterations when message passing (MP) algorithms are employed. Simulation results demonstrate that our proposed new T-tolerance criterion can greatly reduce the average iteration number (complexity) while the decoding performance degradation is controlled within 0.1 dB in the low bit-energy-to-noise-spectral-density ratio (Eb/N0) scenarios.