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

Reliability Ratio Based Weighted Bit-Flipping Decoding for LDPC Codes

In this contribution, a novel reliability-ratio based weighted bit-flipping(RRWBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes. The RRWBF algorithm proposed is benchmarked against the conventional weighted bit-flipping (WBF) algorithm [1] and the improved weighted bit-flipping (IWBF) algorithm [2]. More than 1 and 2 dB coding gain was achieved at an BER of 10-5 while invoking the RRWBF algorithm in comparison to the two benchmarking schemes, when communicating over an AWGN and an uncorrelated Rayleigh channel, respectively. Furthermore, the decoding complexity of the proposed RRWBF algorithm is maintained at the same level as that of the conventional WBF algorithm

Finite Length Analysis of LDPC Codes

In this paper, we study the performance of finite-length LDPC codes in the waterfall region. We propose an algorithm to predict the error performance of finite-length LDPC codes over various binary memoryless channels. Through numerical results, we find that our technique gives better performance prediction compared to existing techniques.Comment: Submitted to WCNC 201