This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability. To overcome this problem, this paper proposes two methods. One is to use a parity check matrix of the echelon canonical form as the starting check matrix of RmFC. The other is to use a parity check matrix that is concatenation (ConC) of multiple parity check matrices. For BCH(31,11,11) code, SPA with ConC realizes Eb/No 3.7 dB better at bit error rate 10-5 than the original SPA, and 3.1 dB better than the SPA with only RmFC.

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.

In this paper, we propose a method for constructing quasi-cyclic low-density parity-check codes randomly using cyclic shift submatrices on the basis of the girth of the Tanner graphs of these codes. We consider (3, K)-regular codes and first derive the necessary and sufficient conditions for weight-4 and weight-6 codewords to exist. On the basis of these conditions, it is possible to estimate the probability that a random method will generate a (3, K)-regular code with a minimum distance less than or equal to 6, and the proposed method is shown to offer a lower probability than does conventional random construction. Simulation results also show that it is capable of generating good codes both regular and irregular.

In this letter, some more concrete trellis relations between a lattice and its dual lattice are firstly given. Based on these relations, we generalize the main results of [1].

In this paper, we investigate Tanner's lower bound for the minimum distance of regular LDPC codes based on combinatorial designs. We first determine Tanner's lower bound for LDPC codes which are defined by modifying bipartite graphs obtained from combinatorial designs known as Steiner systems. Then we show that Tanner's lower bound agrees with or exceeds conventional lower bounds including the BCH bound, and gives the true minimum distance for some EG-LDPC codes.

A parity check matrix for a binary linear code defines a bipartite graph (Tanner graph) which is isomorphic to a subgraph of a factor graph which explains a mechanism of the iterative decoding based on the sum-product algorithm. It is known that this decoding algorithm well approximates MAP decoding, but degradation of the approximation becomes serious when there exist cycles of short length, especially length 4, in Tanner graph. In this paper, based on the generating idempotents, we propose some methods to design parity check matrices for cyclic codes which define Tanner graphs with no cycles of length 4. We also show numerically error performance of cyclic codes by the iterative decoding implemented on factor graphs derived from the proposed parity check matrices.