Construction of quasi-cyclic LDPC cycle codes over Galois Field GF(q) based on cycle entropy and application on patterned media storage

Low-density parity-check (LDPC) codes which were proposed in 1962 had been proved to approach the Shannon limit performance. Due to the superior performance, LDPC codes have got wide applications in information transmission and magnetic recording. Meanwhile, good codes usually bear good performance, such as irregular quasi-cyclic LDPC, so it is valuable to study deeply the construction of LDPC codes. In this digest, we focus on the construction of a type of quasi-cyclic LDPC codes, called cycle codes whose parity-check matrix has exactly weight-2 columns. Based on our previous work, the Maximum Cycle Entropy(MCE) Algorithm for constructing nonbinary LDPC codes is then improved and extended to its quasi-cyclic form (QC-MCE), which maintains the quasi-cyclic structure of the parity-check matrix. With this method employed, an elegant distribution of nonzero entries over the Galois Field GF(q) can be obtained among the cycles whose length is related to the girth. Thus, the independence of probabilistic information transferred during decoding is increased, leading to a better performance. Through comparisons and convergence analyses we find that the proposed QC-MCE algorithm behaves much better than the conventional random one and performs as well as the existing method over the AWGN channel. The decoding complexity of our proposed codes is reasonably low due to the QC structure of the codes. The codes constructed with the proposed method can be well applied over the patterned media storage.