A Unified Decoding Algorithm for Linear Codes Based on Partitioned Parity-Check Matrices

In this paper, we propose a unified decoding algorithm for linear codes, named doubly extended sum-product algorithm (DESPA). The DESPA is described as a belief propagation algorithm over a generalized normal graph that represents the code based on a partitioned parity-check matrix. In one extreme case, the DESPA minimizes the frame-error-rate; while in another extreme case, the DESPA minimizes the bit-error-rate. In practice, the DESPA can be implemented to make trade-offs between decoding complexity and decoding performance.