Tree-Permutation-Matrix Based LDPC Codes

Low-density parity-check (LDPC) codes are normally categorized into random structure or regular structure. In this brief, we introduce a new type of LDPC codes which is of semi-regular style. The parity-check matrices of the new LDPC code type are composed of sub-matrices termed tree-permutation matrices (TPMs). These TPMs are "semi-regular" and are constructed in a systematic way. Using the 2 x 2 identity matrix and anti-diagonal matrix as an example, we illustrate how 2(M) x 2(M ) TPMs are formed. During the formation of the 2(M) x 2(M) TPMs, we further apply the hill-climbing algorithm to avoid short cycles. Finally, we construct a girth-8 TPM-LDPC code with a base matrix of size 4 x 24 and a girth-10 TPM-LDPC code with a base matrix of size 3 x 10. We implement the TPM-LDPC decoders on an FPGA and compare the simulation results and decoder complexity with other LDPC codes.