A low-weight trellis based decoding algorithm for binary linear block codes with application to generalized irregular low-density codes

In this paper, reduced-complexity trellis-based soft-input soft-output (SISO) decoding of linear block codes is considered. A new low-weight subtrellis based SISO decoding algorithm for linear block code to achieve near optimal error performance with a significant reduction in decoding complexity is presented. The proposed scheme is suitable for iterative decoding of linear block codes when used as component codes in compound or concatenated coding schemes. It has the following important features. An initial candidate codeword is first generated by a simple decoding method that guarantees a successful decoding. A low-weight subtrellis diagram centered around the candidate codeword is constructed. The maximum a posteriori probability (MAP) algorithm is then applied to the subtrellis. The generated extrinsic information is then used as a priori information to improve the generation of a candidate codeword for the next stage of iteration. Simulation results in the case of the newly introduced generalized irregular low-density (GILD) codes indicate that the proposed algorithm achieves practically optimal performance with a significant reduction in decoding complexity.