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IEEE International Advance Computing Conference

Analysis of hard decision and soft decision decoding algorithms of LDPC codes in AWGN

Rinu Jose, Ameenudeen Pe

Published Jun 1, 2015• 40 citations
Publisher

Abstract

This article compares the Bit Error Rate (BER) performance of soft and hard decision decoding algorithms of LDPC codes on AWGN channel at different code rates and Signal to Noise Ratio (SNR) levels. Even though, hard decision decoding algorithm is computationally simple, its BER performance is not appreciable. Devising soft decision decoding algorithms which are simple and good in BER performance requires comparison of probabilistic and log domain methods. Towards this, a code word is generated through modulo(2) addition between message bits and generator matrix. After Binary Phase Shift Keying (BPSK) modulation the AWGN noise is introduced to the modulated code word. BER performance is computed by comparing the message decoded by soft and hard decision algorithms with the transmitted message. The experiment is conducted in MATLAB. Soft decision decoding algorithm in log domain provides better BER performance than hard decision decoding algorithm regardless of the SNR level.

DOI
10.1109/iadcc.2015.7154744

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This article compares the Bit Error Rate (BER) performance of soft and hard decision decoding algorithms of LDPC codes on AWGN channel at different code rates and Signal to Noise Ratio (SNR) levels. Even though, hard decision decoding algorithm is computationally simple, its BER performance is not appreciable. Devising soft decision decoding algorithms which are simple and good in BER performance requires comparison of probabilistic and log domain methods. Towards this, a code word is generated through modulo(2) addition between message bits and generator matrix. After Binary Phase Shift Keying (BPSK) modulation the AWGN noise is introduced to the modulated code word. BER performance is computed by comparing the message decoded by soft and hard decision algorithms with the transmitted message. The experiment is conducted in MATLAB. Soft decision decoding algorithm in log domain provides better BER performance than hard decision decoding algorithm regardless of the SNR level.
Under the condition of the Additive White Gaussian Noise(AWGN) channel,both the hard and soft decision decoding algorithms suitable for LDPC codes are simulated and comparatively analyzed based on analyzing the decoding algorithm for LDPC codes.The variable message correlation for Log-Likelihood-Ratio Belief-Propagation(LLR-BP) algorithm in soft decision algorithm is decreased by introducing a multiplicative correction factor.The simulation results show that the decoding error-correction performance of the modified LLR-BP algorithm is greatly improved with little increase of computing complexity.
The article presents a comparative study of LDPC decoding algorithms in an additive white Gaussian noise (AWGN) channel. The aim is to identify the most efficient algorithms for reliable data transmission. Simulations were carried out using the AFF3CT tool with BPSK modulation. Several decoders were analyzed, including GALA, GALB, GALE, PPBF, WBF and MWBF. Performance was evaluated by bit error rate (BER) and frame error rate (FER). The results show that the GalE decoder achieves the best error-correction performance for long codewords (length 20480), with BER values reaching 10-5 and 10-10. For shorter code lengths, MWBF and GalE algorithms also demonstrate good results, with MWBF reaching BER ≈ 10-3 at SNR = 7 dB. In resource-limited conditions, simplified bit-flipping algorithms can provide reasonable efficiency
Low density parity check codes nowadays use in modern system due to their excellent performance. There are different message passing algorithm for LDPC codes to decode. In this paper, we have mention bit flip algorithm in brief and gave its bit error performance over AWGN channel via simulation result. For this communication, we use BPSK i.e. Binary phase shift keying digital modulation technique. This algorithm is based on binary decision message passing algorithm. This paper shows bit error performance of bit flip algorithm for different block lengths of LDPC code. The significance of showing bit error performance in this paper is that it shows how efficiently this algorithm works. We have also mention why BPSK modulation technique is more efficient than any other modulation technique.
Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hot-spot in the field of channel coding in recent years and has a wide range of application prospects in optical communication systems. In this paper, the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate (BER) of LDPC codes. The computer simulation was carried out under additive white Gaussian noise (AWGN) channel and binary phase shift keying (BPSK) modulation. Through theoretical analysis and simulation results, this paper explores the way of multi-rate LDPC decoding.
Forward error correction code with Low Density Parity Check (LDPC) gives substantial results very close to Shannon limit. This can be achieved when complexity and delay time is unlimited. Thus, it is significant to recognize the limitation of those parameters in the decoding of LDPC. In this research, a study of LDPC performance with three decoding algorithms namely; bit-flipping, log domain, and prob domain are presented. The first one is related to hard decision family while the last two types are the soft decision that follows the sum-product algorithm. A simulation model of a wireless communication system included LDPC are evaluated with the motioned three types of decoding using Matlab Package, version 2018a. The results show that the log domain and prob domain are outperforming the bit-flipping algorithm by a significant amount of Signal to Noise Ratio (SNR). Finally, optimum values of LDPC parameters are chosen according to the achieved results that will give better results are presented.
It is proved that hard decision algorithms are more appropriate than a soft decision for low-density parity-check (LDPC) decoding since they are less complex at the decoding level. On the other hand, it is notable that the soft decision algorithm outperforms the hard decision one in terms of the bit error rate (BER) gap. In order to minimize the BER and the gap between these two families of LDPC codes, a new LDPC decoding algorithm is suggested in this paper, which is based on both the normalized min-sum (NMS) and modified-weighted bit-flipping (MWBF). The proposed algorithm is named normalized min sum- modified weighted bit flipping (NMSMWBF). The MWBF is executed after the NMS algorithm. The simulations show that our algorithm outperforms the NMS in terms of BER at 10-8 over the additive white gaussian noise (AWGN) channel by 0.25 dB. Furthermore, the proposed NMSMWBF and the NMS are both at the same level of decoding difficulty.