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New Decoding Scheme for LDPC Codes Based on Simple Product Code Structure  

Shin, Beomkyu (Department of Electrical and Computer Engineering, INMC, Seoul National University, Samsung Electronics, Co., Ltd.)
Hong, Seokbeom (Department of Electrical and Computer Engineering, INMC, Seoul National University, Samsung Electronics, Co., Ltd.)
Park, Hosung (Department of Electrical and Computer Engineering, INMC, Seoul National University, School of Electronics and Computer Engineering, Chonnam National University)
No, Jong-Seon (Department of Electrical and Computer Engineering, INMC, Seoul National University)
Shin, Dong-Joon (Department of Electronic Engineering, Hanyang University)
Publication Information
Journal of Communications and Networks / v.17, no.4, 2015 , pp. 351-361 More about this Journal
Abstract
In this paper, a new decoding scheme is proposed to improve the error correcting performance of low-density parity-check (LDPC) codes in high signal-to-noise ratio (SNR) region by using post-processing. It behaves as follows: First, a conventional LDPC decoding is applied to received LDPC codewords one by one. Then, we count the number of word errors in a predetermined number of decoded codewords. If there is no word error, nothing needs to be done and we can move to the next group of codewords with no delay. Otherwise, we perform a proper post-processing which produces a new soft-valued codeword (this will be fully explained in the main body of this paper) and then apply the conventional LDPC decoding to it again to recover the unsuccessfully decoded codewords. For the proposed decoding scheme, we adopt a simple product code structure which contains LDPC codes and simple algebraic codes as its horizontal and vertical codes, respectively. The decoding capability of the proposed decoding scheme is defined and analyzed using the parity-check matrices of vertical codes and, especially, the combined-decodability is derived for the case of single parity-check (SPC) codes and Hamming codes used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error correcting capability in high SNR region with little additional decoding complexity, compared with the conventional LDPC decoding scheme.
Keywords
Combined-decodability; decoding; low-density parity-check (LDPC) codes; post-processing; product codes;
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