Decoding algorithms for LDPC codes transmitted over channels with ISI

Summary form only given. LDPC (low density parity check) codes (Gallager (1963)) are linear parity check codes with a sparse parity check matrix. In our work Gallager´s original decoding algorithm is extended to alleviate the problem of channel with finite memory. Two decoding algorithms are derived. The basic algorithm tracks the original derivation of Gallager with the necessary adaptations. This results in a single usage of the BCJR algorithm, whereas the iterative part remains intact.. The second algorithm is a generalization of the first. While the basic algorithm only utilizes the correlation among adjacent digits to achieve an improved estimation of the prior probabilities, the generalized algorithm also exploits the information lying in the parity checks in which the adjacent digits participate. This results in modified rightbound messages. The generalized algorithm is asymptotically optimal in the sense of achieved bit error rate based on the information extracted from a given number of adjacent digits.