JOURNAL OF APPLIED MATHEMATICS, 2013(970126) 1-10, 2013 Peer-reviewed
Approximate calculation of channel log-likelihood ratio (LLR) for wireless channels using Pade approximation is presented. LLR is used as an input of iterative decoding for powerful error-correcting codes such as low-density parity-check (LDPC) codes or turbo codes. Due to the lack of knowledge of the channel state information of a wireless fading channel, such as uncorrelated fiat Rayleigh fading channels, calculations of exact LLR for these channels are quite complicated for a practical implementation. The previous work, an LLR calculation using the Taylor approximation, quickly becomes inaccurate as the channel output leaves some derivative point. This becomes a big problem when higher order modulation scheme is employed. To overcome this problem, a new LLR approximation using Pade approximation, which expresses the original function by a rational form of two polynomials with the same total number of coefficients of the Taylor series and can accelerate the Taylor approximation, is devised. By applying the proposed approximation to the iterative decoding and the LDPC codes with some modulation schemes, we show the effectiveness of the proposed methods by simulation results and analysis based on the density evolution.
2012 INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS AND SIGNAL PROCESSING (WCSP 2012), 2012 Peer-reviewed
In this paper, approximate calculation of channel log likelihood ratio (LLR) for wireless channels using Pade approximation is devised. Due to the lack of knowledge of the channel state information of a wireless fading channel, such as uncorrelated flat Rayleigh fading channels, calculation of exact LLR for these channels is quite complicated for a practical implementation. The previous work, LLR calculation using the Taylor approximation, quickly becomes inaccurate as the channel output leaves some derivative point. To overcome this problem, we devise a new LLR approximation using Pade approximation, which expresses the original function by rational form of two polynomials with the same total number of coefficients of the Taylor series, accelerates the Taylor approximation, is devised. By applying the proposed approximation to the iterative decoding and the low-density parity-check codes, we show the effectiveness of the proposed methods by simulation results and analysis based on the density evolution.
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, E92A(10) 2418-2430, Oct, 2009 Peer-reviewed
Two decoding procedures combined with a belief-propagation (BP) decoding algorithm for low-density parity-check codes over the binary erasure channel are presented. These algorithms continue a decoding procedure after the BP decoding algorithm terminates. We derive a condition that our decoding algorithms can correct an erased bit which is uncorrectable by the BP decoding algorithm. We show by simulation results that the performance of our decoding algorithms is enhanced compared with that of the BP decoding algorithm with little increase of the decoding complexity.
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, E91A(10) 2745-2753, Oct, 2008 Peer-reviewed
In this paper, we propose a method for enhancing performance of a sequential version of the belief-propagation (BP) decoding algorithm, the group shuffled BP decoding algorithm for low-density parity-check (LDPC) codes. An improved BP decoding algorithm, called the shuffled BP decoding algorithm, decodes each symbol node in serial at each iteration. To reduce the decoding delay of the shuffled BP decoding algorithm, the group shuffled BP decoding algorithm divides all symbol nodes into several groups. In contrast to the original group shuffled BP, which automatically generates groups according to symbol positions, in this paper we propose a method for grouping symbol nodes which generates groups according to the structure of a Tanner graph of the codes. The proposed method can accelerate the convergence of the group shuffled BP algorithm and obtain a lower error rate in a small number of iterations. We show by simulation results that the decoding performance of the proposed method is improved compared with those of the shuffled BP decoding algorithm and the group shuffled BP decoding algorithm.
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, E91A(10) 2765-2778, Oct, 2008 Peer-reviewed
A new ensemble of low-density parity-check (LDPC) codes for correcting a solid burst erasure is proposed. This ensemble is an instance of a combined matrix ensemble obtained by concatenating some LDPC matrices. We derive a new bound on the critical minimum span ratio of stopping sets for the proposed code ensemble by modifying the bound for ordinary code ensemble. By calculating this bound, we show that the critical minimum span ratio of stopping sets for the proposed code ensemble is better than that of the conventional one with keeping the same critical exponent of stopping ratio for both ensemble. Furthermore from experimental results, we show that the average minimum span of stopping sets for a solid burst erasure of the proposed codes is larger than that of the conventional ones.
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, E89A(10) 2501-2509, Oct, 2006 Peer-reviewed
We study a modification method for constructing low-density parity-check (LDPC) codes for solid burst erasures. Our proposed modification method is based on a column permutation technique for a parity-check matrix of the original LDPC codes. It can change the burst erasure correction capabilities without degradation in the performance over random erasure channels. We show by simulation results that the performance of codes permuted by our method are better than that of the original codes, especially with two or more solid burst erasures.