Analysis of Message-Passing Decoding of Finite-Length Concatenated Codes

We analyze the performance of message-passing decoding of finite-length concatenated codes. We first show that the message-passing decoder is closely related to a dual optimization decoder. The connections between these two decoders are further elucidated by proving that both of them attain the same objective function value of a generalized linear programming decoder in the limit as the signal-to-noise ratio (SNR) goes to infinity. Consequently, the framework of pseudo-weight analysis, which was originally proposed for analyzing the linear programming decoder, can be extended to analyze the performance of the message-passing decoder for finite-length codes. We then derive lower bounds to the pseudo-weights of general concatenated codes by utilizing the special structure of their parity-check matrices. We finally present a method to increase the max-fractional weight by adding redundant parity-check constraints and thereby improving the decoding performance. Simulation studies are carried out to assess the performance of the proposed algorithms and substantiate the theoretic claims.