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Iranian Conference on Electrical Engineering

Low Decoding Complexity of LDPC Codes Over the Binary Erasure Channel

Sareh Majidi Ivari, M. Reza Soleymani, Yousef R. Shayan

Published May 1, 2018• 0 citations
Publisher

Abstract

In this paper, we present a new low complexity decoding algorithm outperforming existing schemes. When the Belief Propagation fails and cannot solve all the erased bits, the guessing algorithm makes assumptions on a set of erased bits. However, in our new algorithm instead of guessing the values of a set of message bits, the decoder selects a set of check nodes and makes assumption on bits connected to them. The number of possibilities is reduced by half because the field is binary resulting in lower decoding complexity. The proposed decoding algorithm is applied to two regular half rate LDPC codes with lengths of 1000 and 2000. The theoretical belief propagation (BP) threshold for these two codes is 0.429. It is shown that the actual BP threshold is improved using the new algorithm. Setting the number of possibilities to two, we achieve a threshold of 0.43 which is higher than the BP theoretical.

DOI
10.1109/icee.2018.8472553

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In this paper, we present a new low complexity decoding algorithm outperforming existing schemes. When the Belief Propagation fails and cannot solve all the erased bits, the guessing algorithm makes assumptions on a set of erased bits. However, in our new algorithm instead of guessing the values of a set of message bits, the decoder selects a set of check nodes and makes assumption on bits connected to them. The number of possibilities is reduced by half because the field is binary resulting in lower decoding complexity. The proposed decoding algorithm is applied to two regular half rate LDPC codes with lengths of 1000 and 2000. The theoretical belief propagation (BP) threshold for these two codes is 0.429. It is shown that the actual BP threshold is improved using the new algorithm. Setting the number of possibilities to two, we achieve a threshold of 0.43 which is higher than the BP theoretical.
In this correspondence, we first investigate some analytical aspects of the recently proposed improved decoding algorithm for low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We derive a necessary and sufficient condition for the improved decoding algorithm to successfully complete decoding when the decoder is initialized to guess a predetermined number of guesses after the standard message-passing terminates at a stopping set. Furthermore, we present improved bounds on the number of bits to be guessed for successful completion of the decoding process when a stopping set is encountered. Under suitable conditions, we derive a lower bound on the number of iterations to be performed for complete decoding of the stopping set. We then present a superior, novel improved decoding algorithm for LDPC codes over the binary erasure channel (BEC). The proposed algorithm combines the observation that a considerable fraction of unsatisfied check nodes in the neighborhood of a stopping set are of degree two, and the concept of guessing bits to perform simple and intuitive graph-theoretic manipulations on the Tanner graph. The proposed decoding algorithm has a complexity similar to previous improved decoding algorithms. Finally, we present simulation results of short-length codes over BEC that demonstrate the superiority of our algorithm over previous improved decoding algorithms for a wide range of bit error rates
Two decoding procedures combined with a belief-propagation (BP) decoding algorithm for low-density parity-check codes over the binary erasure channel are presented. These algorithms continue a decoding procedure after the BP decoding algorithm terminates. We derive a condition that our decoding algorithms can correct an erased bit which is uncorrectable by the BP decoding algorithm. We show by simulation results that the performance of our decoding algorithms is enhanced compared with that of the BP decoding algorithm with little increase of the decoding complexity.
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, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.
An improved belief propagation(BP) decoding scheme was put forward to solve the high complexity and low decoding efficiency problem of BP in low density parity check(LDPC) codes.Because different bit nodes and check nodes have different reliability and contribute differently to BP decoding;the proposed decoding scheme employs a differentiate rule based on lawless check number and pseudo posterior probability to evaluate every bit's reliability before each step of iteration;The nodes have little lawless check number and large pseudo posterior probability are supposed to have higher reliability.The bits with high reliability need not to be updated by the decoder.Simulation shows that the proposed BP decoding algorithm can reduce the computational load and increase the decoding efficiency significantly.
This paper presents a new improved decoding algorithm for low-density parity-check (LDPC) codes over the binary erasure channel (BEC). The proposed algorithm combines the fact that a considerable fraction of unsatisfied check nodes are of degree two with the concept of guessing bits to perform simple graph-theoretic manipulations on the Tanner graph. The proposed decoding algorithm has a complexity similar to present improved decoding algorithms [H. Pishro-Nik et al., 2004]. Simulations of codes of very short lengths over BEC reveal the superiority of our algorithm over present improved decoding algorithms for a wide range of bit error rates.