The low-density parity-check codes based on The n-queen problem

Abstract

This paper presents a new family of low-density parity-check (LDPC) code, the sparse parity-check matrix of which is constructed by self-defining non-diagonal identity sub-matrix that is a solution of the "n-queen problem". So this sub-matrix is called the Q-matrix and these LDPC codes are called the Q-matrixes LDPC codes. The Q-matrixes LDPC codes are good or very good codes with iterative decoding and their Tanner graphs are free of 4-lines cycle. Furthermore, they can be created in cycle form. Their encoding can be achieved in linear time. Especially, their code length and code rate can be flexible and quickly adjusted according to the practical situation, and the performance of high rate is also very good. The other unique excellence is that the large sparse parity-check matrixes of long Q-matrixes LDPC codes require very small storage space. The result of this paper is very significant not only for designing low complexity encoder, improving performance and reducing the complexity of the sum-product iterative decoding algorithm, but also for building practice system of encodable and decodable LDPC code.