Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on Information Theor

Iterative Soft-Input Soft-Output Decoding with Ordered Reliability Bits GRAND

Guessing Random Additive Noise Decoding (GRAND) is a universal decoding algorithm that can be used to perform maximum likelihood decoding. It attempts to find the errors introduced by the channel by generating a sequence of possible error vectors in order of likelihood of occurrence and applying them to the received vector. Ordered reliability bits GRAND (ORBGRAND) integrates soft information received from the channel to refine the error vector sequence. In this work, ORBGRAND is modified to produce a soft output, to enable its use as an iterative soft-input soft-output (SISO) decoder. Three techniques specific to iterative GRAND-based decoding are then proposed to improve the error-correction performance and decrease computational complexity and latency. Using the OFEC code as a case study, the proposed techniques are evaluated, yielding substantial performance gain and astounding complexity reduction of 48\% to 85\% with respect to the baseline SISO ORBGRAND.Comment: Submitted to Globecom 202

Soft-output decoding algorithms in iterative decoding of turbo codes

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed

Design and optimization of joint iterative detection and decoding receiver for uplink polar coded SCMA system

SCMA and polar coding are possible candidates for 5G systems. In this paper, we firstly propose the joint iterative detection and decoding (JIDD) receiver for the uplink polar coded sparse code multiple access (PC-SCMA) system. Then, the EXIT chart is used to investigate the performance of the JIDD receiver. Additionally, we optimize the system design and polar code construction based on the EXIT chart analysis. The proposed receiver integrates the factor graph of SCMA detector and polar soft-output decoder into a joint factor graph, which enables the exchange of messages between SCMA detector and polar decoder iteratively. Simulation results demonstrate that the JIDD receiver has better BER performance and lower complexity than the separate scheme. Specifically, when polar code length N=256 and code rate R=1/2 , JIDD outperforms the separate scheme 4.8 and 6 dB over AWGN channel and Rayleigh fading channel, respectively. It also shows that, under 150% system loading, the JIDD receiver only has 0.3 dB performance loss compared to the single user uplink PC-SCMA over AWGN channel and 0.6 dB performance loss over Rayleigh fading channel

EXIT (EXtrinsic Information Transfer) Chart Analysis for BCH (Bose-Chaudhuri- Hocquenghem) Codes

BCH (Bose-Chaudhuri-Hocquenghem) codes are used extensively in numerous applications in order to achieve reliable data transfer. In this paper, the parameters of BCH codes are introduced and used to investigate its applications, characteristics and performance when employed as inner and outer code in decoding method. To evaluate the parameters, three types of BCH codes: (7,4,3), (15,11,3) and (31,26,3); are applied. In addition, the implementation of BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm is discussed by applying APP-SISO (a posteriori probabilities – Soft Input Soft Output) decoding for BCH codes. The proposed cheme employing inner and outer decoding of BCH codes is analyzed and compared by using EXIT characteristic of BCH decoders. The channel capacity measurements for different rates inner BCH codes are described by using BPSK modulation over AWGN channel. Lastly, the BER performances of BCH codes are observed for different types, in order to obtain better performance of BER plot indeed

EXIT (EXtrinsic Information Transfer) Chart Analysis for BCH (Bose-Chaudhuri- Hocquenghem) Codes

BCH (Bose-Chaudhuri-Hocquenghem) codes are used extensively in numerous applications in order to achieve reliable data transfer. In this paper, the parameters of BCH codes are introduced and used to investigate its applications, characteristics and performance when employed as inner and outer code in decoding method. To evaluate the parameters, three types of BCH codes: (7,4,3), (15,11,3) and (31,26,3); are applied. In addition, the implementation of BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm is discussed by applying APP-SISO (a posteriori probabilities – Soft Input Soft Output) decoding for BCH codes. The proposed cheme employing inner and outer decoding of BCH codes is analyzed and compared by using EXIT characteristic of BCH decoders. The channel capacity measurements for different rates inner BCH codes are described by using BPSK modulation over AWGN channel. Lastly, the BER performances of BCH codes are observed for different types, in order to obtain better performance of BER plot indeed

Soft-Output Deep Neural Network-Based Decoding

Deep neural network (DNN)-based channel decoding is widely considered in the literature. The existing solutions are investigated for the case of hard output, i.e. when the decoder returns the estimated information word. At the same time, soft-output decoding is of critical importance for iterative receivers and decoders. In this paper, we focus on the soft-output DNN-based decoding problem. We start with the syndrome-based approach proposed by Bennatan et al. (2018) and modify it to provide soft output in the AWGN channel. The new decoder can be considered as an approximation of the MAP decoder with smaller computation complexity. We discuss various regularization functions for joint DNN-MAP training and compare the resulting distributions for [64, 45] BCH code. Finally, to demonstrate the soft-output quality we consider the turbo-product code with [64, 45] BCH codes as row and column codes. We show that the resulting DNN-based scheme is very close to the MAP-based performance and significantly outperforms the solution based on the Chase decoder. We come to the conclusion that the new method is prospective for the challenging problem of DNN-based decoding of long codes consisting of short component codes.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl