CTH08-4: Protograph LDPC Codes with Node Degrees at Least 3

In this paper we present protograph codes with degree-3 nodes and one high degree node. The iterative decoding threshold for proposed rate 1/2 codes are lower, by about 0.2 dB, than the best known irregular LDPC codes with degree at least 3. The main motivation is to construct rate-compatible protograph-based LDPC codes for fixed code block length (n) that simultaneously achieve low iterative decoding thresholds and guarantee minimum distance that is linearly increasing with n. We start with a rate 1/2 protograph LDPC code with degree-3 nodes and one high degree node. Higher rate codes are obtained by connecting check nodes with degree-2 non-transmitted nodes. This is equivalent to constraint combining in the protograph. The condition where all constraints are combined corresponds to the highest rate code. Through examples we show that iterative decoding thresholds as low as 0.544 dB can be achieved for small protographs with node degrees at least three. FPGA simulation results show that the proposed family of codes perform as predicted.