Design of nonbinary LDPC cycle codes based on cycle entropy

In this paper, we focus on the design of a type of low-density parity-check (LDPC) codes called cycle codes whose parity-check matrix have exactly weight-2 columns. An approach to design nonbinary LDPC cycle codes with good performance is presented based on cycle entropy defined here. This method can obtain an elegant distribution of the nonbinary elements over the Galois Field GF(q) among the cycles whose length is exactly equal to the girth. Simulation results demonstrate that the LDPC codes designed with the proposed algorithm perform better than the randomly-constructed nonbinary LDPC cycle codes.