Low-density generator matrix codes for indoor and Markov channels

We propose a modified algorithm for the decoding of linear codes with low-density generator matrix (LDGM) codes (a class of LDPC codes) over indoor and finite-state binary Markov channels. In order to avoid error floors, a concatenation of two LDGM codes is utilized. The hidden Markov model representing the channel is incorporated into the graph corresponding to the LDGM codes, and the message passing algorithm is modified accordingly. The proposed scheme clearly outperforms systems in which the channel statistics are not exploited in the decoding process, allowing reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. Moreover, the proposed method can be successfully applied for real wireless channels that can be modeled with hidden Markov models, such as indoor channels.