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IEEE Communications Letters

New Stopping Criterion for Fast Low-Density Parity-Check Decoders

Tian Xia, Hsiao‐Chun Wu, Hong Jiang

Published Aug 21, 2014• 15 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2014.2349988

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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.
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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.
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.
An early stopping criterion for low-density parity-check decoding is proposed to reduce the number of decoding iterations. The proposed early stopping criterion 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. 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% iteration for decoding at low to medium Eb/N0, compared with the existing method.
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.
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.