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A Differential Binary Message-Passing LDPC Decoder

Nastaran Mobini, Amir H. Banihashemi, Saied Hemati

Published Nov 1, 2007• 16 citations
Publisher

Abstract

In this paper, we propose a binary message-passing algorithm for decoding low-density parity-check (LDPC) codes. The algorithm substantially improves the performance of purely hard-decision iterative algorithms with a small increase in the memory requirements and the computational complexity. We associate a reliability value to each nonzero element of the code's parity-check matrix, and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes. For the tested random and finite-geometry LDPC codes, the proposed algorithm can achieve performance as close as 1.3 dB and 0.7 dB to that of belief propagation (BP) at the error rates of interest, respectively. This is while, unlike BP, the algorithm does not require the estimation of channel signal to noise ratio. Low memory and computational requirements and binary message-passing make the proposed algorithm attractive for high-speed low-power applications.

DOI
10.1109/glocom.2007.300

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In this paper, we propose a binary message-passing algorithm for decoding low-density parity-check (LDPC) codes. The algorithm substantially improves the performance of purely hard-decision iterative algorithms with a small increase in the memory requirements and the computational complexity. We associate a reliability value to each nonzero element of the code's parity-check matrix, and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes. For the tested random and finite-geometry LDPC codes, the proposed algorithm can achieve performance as close as 1.3 dB and 0.7 dB to that of belief propagation (BP) at the error rates of interest, respectively. This is while, unlike BP, the algorithm does not require the estimation of channel signal to noise ratio. Low memory and computational requirements and binary message-passing make the proposed algorithm attractive for high-speed low-power applications.
In this paper, we propose a binary message-passing algorithm for decoding low-density parity-check (LDPC) codes. The algorithm substantially improves the performance of purely hard-decision iterative algorithms with a small increase in the memory requirements and the computational complexity. We associate a reliability value to each nonzero element of the code's parity-check matrix, and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes. For the tested random and finitegeometry LDPC codes, the proposed algorithm can perform as close as about 1 dB and 0.5 dB to belief propagation (BP) at the error rates of interest, respectively. This is while, unlike BP, the algorithm does not require the estimation of channel signal to noise ratio. Low memory and computational requirements and binary message-passing make the proposed algorithm attractive for high-speed low-power applications.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
In the information theory , the non- binary low density parity check  (NB-LDPC) code is a  linear error correcting code , a method of transmitting message over a  noisy transmission channel. LDPCcodes are  capacity-approaching codes , which  means  that  practical constructions exist  that allow the noise threshold to be set very close to the theoretical maximum for a symmetric memory less channel.Using iterative  belief propagation techniques, NB-LDPC codes can be decoded in time linear to their block length. Non-binary low-density parity-check codes can achieve higher performance than their binary counterparts. Recently, two algorithms were developed for decoding NB-LDPC codes: iterative hard reliability-based majority-logic decoding (IHRB-MLGD) and iterative soft reliability-based majority-logic decoding (ISRB-MLGD has better performance-complexity tradeoffs than previous algorithms. This paper first proposes message-passing in such a way that we can reduce the memory consumption to a greater extent at the same time there should not be performance loss. By using enhanced iterative reliability-based majority-logic decoding algorithms we can achieve effective complexity-performance and noise free design. Compared to previous designs, our proposed decoders have at least tens of times lower complexity with moderate coding gain loss.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.
Introduced is a new type of message-passing (MP) decoders for low-density parity-check (LDPC) codes over the binary symmetric channel. Unlike traditional belief propagation (BP) based MP algorithms which propagate probabilities or log-likelihoods, the new MP decoders propagate messages requiring only a finite number of bits for their representation in such a way that good performance in the error floor region is ensured. Additionally, these messages are not quantised probabilities or log-likelihoods. As examples, MP decoders are provided that require only three bits for message representation, but surpass the floating-point BP (which requires a large number of bits for representation) in the error-floor region.
Binary message passing decoders for low-density parity-check codes are studied by using extrinsic information transfer charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the log-likelihood ratio (L-value) domain. A hard decision results in the Gallager B algorithm and examples show that increasing the channel output alphabet to two bits gains more than 1.0 dB in signal to noise ratio when using optimized codes. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.