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International Conference on Computer and Information Technology (ICCIT)

Combined normalized and offset extended min sum decoding algorithm for LDPC codes over GF (q)

Md Murad Hossain, Mohammad Rakibul Islam

Published Dec 1, 2011• 0 citations
Publisher

Abstract

In this paper the combined normalized and offset extended min sum (EMS) is proposed for efficient decoding of non-binary low density parity check (LDPC) codes. EMS is the approximation of the sum product algorithm for reducing the computation complexity. However there is a performance gap between EMS and SP algorithm due to this approximation. The approximate check node messages of the extended min sum are compensated by both normalized and offset factor. The normalized factor and offset factor is determined for one iteration and is kept constant for all SNRs and iterations. It will shown in bit error rate simulation of (1008, 504) LDPC code over GF (4) that combined normalized offset extended min sum has superior performance than normalized and offset extended min sum. However, it requires only extra one multiplication for each cycle.

DOI
10.1109/iccitechn.2011.6164866

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In this paper the combined normalized and offset extended min sum (EMS) is proposed for efficient decoding of non-binary low density parity check (LDPC) codes. EMS is the approximation of the sum product algorithm for reducing the computation complexity. However there is a performance gap between EMS and SP algorithm due to this approximation. The approximate check node messages of the extended min sum are compensated by both normalized and offset factor. The normalized factor and offset factor is determined for one iteration and is kept constant for all SNRs and iterations. It will shown in bit error rate simulation of (1008, 504) LDPC code over GF (4) that combined normalized offset extended min sum has superior performance than normalized and offset extended min sum. However, it requires only extra one multiplication for each cycle.
In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.
The extended min-sum algorithm (EMS) for decoding non-binary low density parity check (NB-LDPC) codes reduces the decoding complexity by truncating the message vector by retaining only the most reliable symbols. However, the EMS algorithm does not consider that the noise of the received codeword is gradually reduced as the iteration count goes up. In this paper, we propose a low-complexity adaptive EMS algorithm, called threshold-based EMS (TB-EMS). The TB-EMS algorithm has a simple adaptive rule to calculate the new message vector length compared to the A-EMS. The proposed algorithm selects one of two message vector lengths. Experimental results show that the proposed algorithm reduces the decoding complexity with minimal performance degradation compared with the EMS algorithm. Further, the decoding performance of the TB-EMS is better than A-EMS.
Decoding Algorithms for Nonbinary LDPC Codes Over GF(q)(q)(q)
In this letter, we address the problem of decoding nonbinary low-density parity-check (LDPC) codes over finite fields GF(q), with reasonable complexity and good performance. In the first part of the letter, we recall the original belief propagation (BP) decoding algorithm and its Fourier domain implementation. We show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding. In the second part of the letter, we introduce a simplified decoder which is inspired by the min-sum decoder for binary LDPC codes. We called this decoder extended min-sum (EMS). We show that it is possible to greatly reduce the computational complexity of the check-node processing by computing approximate reliability measures with a limited number of values in a message. By choosing appropriate correction factors or offsets, we show that the EMS decoder performance is quite good, and in some cases better than the regular BP decoder. The optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution. Our simulations on ultra-sparse codes over very-high-order fields show that nonbinary LDPC codes are promising for applications which require low frame-error rates for small or moderate codeword lengths. The EMS decoder is a good candidate for practical hardware implementations of such codes
The decoding algorithms of Nonbinary low-density parity-check (NB-LDPC) codes mainly include Belief Propagation (BP), Fast Fourier Transforms (FFT) and Extended Min-Sum (EMS). Among these decoding algorithms, although EMS has the lowest decoding complexity, there is still room for improvement. Therefore, this paper proposes a new algorithm based on the EMS algorithm to further improve the decoding complexity and performance. In order to reduce complexity, an adaptive truncation rule is added to the decoding process. The adaptive truncation rule chooses the length of automatic truncation to reduce the average number of iterations. Thus, the complexity of decoding algorithm is reduced. Besides the weighting factors is added to the variable update iteration process, which effectively improves the decoding performance. The results show that the proposed algorithm has about 0.9 dB gain compared with the EMS decoding algorithm when the bit error rate (BER) is 10--4and the Galois field GF(q) (q16).
The extended min-sum (EMS) algorithm is adopted for non-binary low density parity check (NB-LDPC) codes. The high complexity of EMS algorithm is a hot topic in recent years. Aiming at the problem, a low-complexity EMS algorithm based on NB-LDPC codes is proposed. Dynamic bubble-check (DBC) algorithm in elementary check node (ECN) steps is adopted to reduce the complexity of check node. Furthermore, the proposed algorithm dynamically truncates the length of the message vector by the number of decoding iterations. Taking the length of message vector truncated again as half of the original one as an example, the simulation results and complexity are analyzed. Analysis shows that, compared to the EMS algorithm, computational complexity of comparisons and real additions of check node of the proposed algorithm have reduced by about 70% and 25% respectively. Meantime, the decoding performance of the proposed algorithm approach that of EMS algorithm and the loss is only near 0.08 dB when the bit error rate (BER) is 10−3and the Galois fieldGF(q)(q=16)GF(q)(q=16)GF(q)(q=16).
This letter focuses on the improvement in the error correction performance of the extended min-sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, we propose a novel threshold-based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the method’s complexity.