Construction of QC LDPC Cycle Codes Over GF( ${q}$ ) Based on Cycle Entropy and Applications on Patterned Media Storage

In this paper, we focus on the construction of a type of quasi-cyclic low-density-parity-check (QC LDPC) codes called cycle codes. Based on our previous work, the maximum cycle entropy (MCE) algorithm for constructing nonbinary LDPC codes can be extended to its QC form (QC-MCE), which maintains the QC 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. Extensive simulation results show that the proposed QC-MCE algorithm behaves much better than the conventional random one and performs as well as the existing method over a pattern media channel with both additive white Gaussian noise (AWGN) and transition jitter noise (TJN). 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.