Methods for coding and decoding LDPC codes, and method for forming LDPC parity check matrix

摘要

Provided are methods for encoding and decoding low-density parity-check (LDPC) codes and a method for forming an LDPC parity check matrix. The method for forming the LDPC parity check matrix, includes the steps of: preparing a plurality of parity check matrixes; and selecting a parity check matrix having maximum performance from the prepared parity check matrixes, wherein the parity check matrix has a degree distribution G(x) that meets an equation,; $$ G\left(x\right)=\stackrel{d_i-1}{\sum _{k=2}}{a}_k{x}^k+\stackrel{d_{\max }}{\sum _{k=d_i}}C{k}^{-\gamma }{x}^k\mathrm{or}G\left(x\right)=\stackrel{d_{\max }}{\sum _{k=2}}{C\left(k+\alpha \right)}^{-\gamma }{x}^k,$$where, a_k is a parameter that corresponds to the probability that nodes of the graph have a degree k, C is a parameter that is determined by a normalization condition, G(1)=1, and α, γ are parameters that is optimized through numerical calculations. This may significantly decrease a time to discover an optimal code by using a power-law distribution with less parameters in designing the LDPC codes, as compared with numerical optimization in a global parameter space.