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International Conference on Advanced Communication Systems and Information Security (ACOSIS)

Novel method for improving performances of normalized MS decoder using WIMAX code

Abdelilah Kadi, Mostafa Mrabti, Saïd Najah, Emmanuel Boutillon

Published Oct 1, 2016• 1 citation
Publisher

Abstract

LDPC code is a powerful error correcting code used in many communication systems. Efficient decoding algorithm and hardware implementation of LDPC code is an important issue. The paper proposes an improved version of the Normalized Min-Sum (NMS) decoding algorithm named “Girth-Aware NMS”. The principle of the GA-NMS is to determine “offline” the optimal normalisation factor of the extrinsic message using the structure property of the Tanner Graph associated to the LDPC matrix. The idea can be expressed simply: a check node implied in one, or more, cycle of minimum size (the so-called Girth) in the Tanner Graph is more subjected to self-confirmation than other check nodes. Thus, the extrinsic messages generated by this type of check nodes should be more aggressively “normalized” (or attenuated) than other check nodes. In the context of the IEEE P802.16e standard (WIFI standard), simulation results of the GA-NMS shows both improved decoding performance and reduced average number of decoding iterations.

DOI
10.1109/acosis.2016.7843926

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LDPC code is a powerful error correcting code used in many communication systems. Efficient decoding algorithm and hardware implementation of LDPC code is an important issue. The paper proposes an improved version of the Normalized Min-Sum (NMS) decoding algorithm named “Girth-Aware NMS”. The principle of the GA-NMS is to determine “offline” the optimal normalisation factor of the extrinsic message using the structure property of the Tanner Graph associated to the LDPC matrix. The idea can be expressed simply: a check node implied in one, or more, cycle of minimum size (the so-called Girth) in the Tanner Graph is more subjected to self-confirmation than other check nodes. Thus, the extrinsic messages generated by this type of check nodes should be more aggressively “normalized” (or attenuated) than other check nodes. In the context of the IEEE P802.16e standard (WIFI standard), simulation results of the GA-NMS shows both improved decoding performance and reduced average number of decoding iterations.
Recently, short block codes are in great demand due to the emergent applications requiring the transmission of a short data unit and can guarantee speedy communication, with a minimum of latency and complexity which are among the technical challenges in today’s wireless services and systems. In the context of channel coding using low density parity check (LDPC) codes, the shorter length LDPC block codes are more likely to have short cycles with lengths of 4 and 6. The effect of the cycle with the minimum size is that this one prevents the propagation of the information in the Tanner graph during the iterative process. Therefore, the message decoded by short block code is assumed to be of poor quality due to short cycles. In this work, we present a study of the evolution of the messages on check nodes during the iterative decoding process when using the LDPC decoding algorithm normalized min sum (NMS), to see the destructive effect of short cycles and justify the effectiveness of the girth aware normalized min sum (GA-NMS) decoding LDPC codes algorithm in terms of correction of the errors, particularly for the codes with short cycles 4 and 6. In addition to this, the GA-NMS algorithm is evaluated in terms of bit error rate performance and convergence behavior, using wireless regional area networks (WRAN) LDPC code, which is considered as a short block code.
In this paper, we present an improvement on the normalized min-sum (NMS) decoding algorithm for low density parity check codes. The modified NMS (M-NMS) algorithm introduces a more efficient adjustment for check node update computation. Taking the sub-minimum value among extrinsic information from the variable nodes into consideration, we make the correction factor varies with different iterations. Results show that, compared with standard min-sum (MS) and NMS decoding algorithms, the proposed method not only offers a better performance but also achieves a lower error floor in the high SNR region.
Low-density parity-check code (LDPC) is a kind of better error correction code which is played an important role in the reliability transmission of communication systems. In the aspect of decoding algorithm, the NMS algorithm becomes the mainstream algorithm dues to its lower complexity. what’s more, the Semi-serial decoding algorithm was put forward to reduce decoding iterations. However, the compensation factor of NMS algorithm is a fixed value and the Semi-serial decoding algorithm only considers one aspect of reducing iterations. In the actual decoding process, this value varies with the degree of the check node and the number of iterations. in order to solve the problems of these algorithms, this paper will propose a new improved algorithm. Firstly, we will adopt a dynamic compensation factor to improve performance of NMS algorithm on regular LDPC code. Then combined with the idea of Semi-serial decoding algorithm to reduce the number of iterations. The dynamic factor is firstly analyzed theoretically by density evolution theory. Then through the Monte Carlo experiment and the true LLR, the suitable dynamic compensation factors can be obtained which is changes with the number of iterations.
For recent years, deep learning has been studied and utilized among decoders in wireless and optical communication. For low density parity check (LDPC) codes, most works use neural network (NN) to implement the belief propagation (BP) decoder and unfold its iterations into layers activated by different functions. However, the whole decoder composed by neural network performs lots of non-linear operations, which are time consuming and unfriendly to hardware implementation. In this work, a neural network-aided normalized min-sum (NN-aided NMS) decoder for LDPC code is proposed, in which the normalization factors are inferred from input log likelihood ratio (LLR) by apre-trained NN, while maintaining check and variable nodes processing the same as in min-sum (MS) decoder. In order to test the proposed decoder with irregular LDPC code, a rate-7/8 one was constructed using progressive edge growth (PEG) algorithm, showing better error correction capability than the standard of consultative committee for space data systems (CCSDS) LDPC (8176,7154) code by 0.08 dB with the same rate. Simulation results show that, NN-aided NMS decoder outperforms MS decoder by 0.3 dB, and its performance approaches BP decoder with a gap of 0.02 dB, which is 50% closer than the best NMS decoder using 0.7 as the normalization factor. The proposed decoder has good performance for both regular and irregular LDPC codes, and needs much less computation complexity than BP decoder. It introduces more linear computation than NMS decoder but achieves better bit error rate (BER) performance, thus becoming a good complement between BP and NMS decoder when trading off among complexity, error correction performance and hardware implementation for wireless and satellite communication.
Low-density parity-check (LDPC) codes are of prime importance in achieving near-Shannon capacity in current communication systems. However, the optimal decoding process for LDPC codes is computationally intensive. This paper presents a neural normalized min-sum (NNMS) decoding network that improves error correction capabilities with minimal computational overhead. A weight-sharing approach is adopted in the NNMS model, in which the correction factors (α, β) are shared across nodes within a single layer. This approach decreases the total number of parameters in the model compared to traditional neural decoders, making it easier for hardware implementation. The NNMS model is tested using a (576, 432) LDPC code for an additive white Gaussian noise channel with binary phase shift keying modulation. Simulation results show that the NNMS model outperforms traditional normalized min-sum (NMS) decoders. At a signal-to-noise ratio of 5 dB, the NNMS model has a bit-error rate (BER) of 1.0 × 10−7, whereas traditional NMS models have a less steep slope. In particular, the NNMS model has a coding gain of 1.25 dB compared to the traditional NMS model at a BER threshold of 1.0 × 10−3. This shows that the NNMS model is an efficient solution for high-performance, real-time digital communication systems.