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IEEE Vehicular Technology Conference

A Stopping Criterion for Low-Density Parity-Check Codes

Donghyuk Shin, Kyoungwoo Heo, Sang-Bong Oh, Jeongseok Ha

Published Apr 1, 2007• 33 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes have an inherent stopping criterion, parity-check constraints (equations). By testing the parity-check constraints, an LDPC decoder can detect successful decoding and stop their decoding, which is, however, not possible with turbo codes. In this paper, we propose a stopping criterion to predict decoding failure of LDPC codes, instead of detecting successful decoding. If the decoder predicts the decoding failure in advance, the receiver can more rapidly response to the transmitter and request for additional parity bits with an automatic repeat request (ARQ) protocol, which reduces overall system latency. The receiver can also save power consumption by avoiding unnecessary decoder iterations. The proposed stopping criterion makes use of the variations of the number of satisfied parity-check constraints in the belief-propagation (BP) decoding which is always tested in the conventional BP decoding to detect successful decoding. Thus, the proposed stopping criterion does not require any additional complexity. The counting of satisfied parity-check constraints shows behaviors of the BP decoding, which comes, otherwise, from the observations of changes of log-likelihood ratio (LLR) values in multi-bit resolution with additional complexity.

DOI
10.1109/vetecs.2007.319

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Low-density parity-check (LDPC) codes have an inherent stopping criterion, parity-check constraints (equations). By testing the parity-check constraints, an LDPC decoder can detect successful decoding and stop their decoding, which is, however, not possible with turbo codes. In this paper, we propose a stopping criterion to predict decoding failure of LDPC codes, instead of detecting successful decoding. If the decoder predicts the decoding failure in advance, the receiver can more rapidly response to the transmitter and request for additional parity bits with an automatic repeat request (ARQ) protocol, which reduces overall system latency. The receiver can also save power consumption by avoiding unnecessary decoder iterations. The proposed stopping criterion makes use of the variations of the number of satisfied parity-check constraints in the belief-propagation (BP) decoding which is always tested in the conventional BP decoding to detect successful decoding. Thus, the proposed stopping criterion does not require any additional complexity. The counting of satisfied parity-check constraints shows behaviors of the BP decoding, which comes, otherwise, from the observations of changes of log-likelihood ratio (LLR) values in multi-bit resolution with additional complexity.
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.
A two-stage decoding algorithm to lower the error-floor for low-density parity-check (LDPC) codes is presented. An efficient stopping criterion is proposed to avoid unnecessary iterations in the first stage. If the stopping criterion is reached, the first stage decoding will be terminated and the second stage decoding will be started, where the unsuccessfully decoded words are re-decoded by manipulating the log-likelihood ratio (LLR) of two types of specifically selected variable nodes. Simulation results show that the proposed algorithm can effectively lower the error floor of LDPC codes while maintaining a low decoding complexity.
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.
The stopping criterion based on parity-check constraints is an inherent advantage of low-density parity-check (LDPC) codes. However, the parity-check computation with signs of the posterior information costs additional hardware or decoding delays, which may be a particular problem for the full-parallel LDPC decoding in optical transmission. Furthermore, the performance degradation caused by using simplified stopping criterions should also be considered, where the maximum number of the iterations is usually limited by the very high decoding speed in optical transmission. In this paper, we propose an efficient early stopping criterion with the consideration of the complexity/performance tradeoffs. The new method is based an intelligent combination of check equations and temporary hard decisions, and can be pipelined with check-node updating, thus leading to lower complexity and power consumption, which are desirable for both optical and wireless communications. Simulation results show that the hybrid criterion not only achieves the same performance as the conventional stopping criterions, but also provides a noticeable gain for the other simplified stopping criterions.