A Novel Method tor Construction of Structured Regular LDPC Codes with Girth Twelve Using Gray Code Representations

摘要

The Low-Density Parity-Check (LDPC) code is a linear block code specified by a parity-check matrix H. The construction process of LDPC codes considers the parameters such as row and column-weights, rate, girth, and code length. Regularity of the codes provides the advantage like simplicity of hardware implementation and fast encoding. Large girth speeds the convergence of iterative decoding and improves performance. To increase girth of a code and avoid short cycles, the parity-check matrix H must be sufficiently sparse, and hence, the block length must be large. Hence, there is a need to develop method of constructing LDPC codes over a wide range of lengths, rates, and girths. In this paper, we introduce a novel method for constructing structured regular LDPC codes with different densities, rates, lengths, and girths using Gray-code representations. The advantage of this algorithm compared to other methods is its flexibility in terms of rates, lengths, and girths. LDPC codes with column-weight two have low computational complexity and are promising for data storage and partial response channels. Hence, a modified version of proposed algorithm, to construct a column-weight two LDPC codes with girth 8 and 12, is also presented in this paper.