Graph-Based Decoding in the Presence of ISI

We propose a new graph representation for ISI channels that can be used for combined equalization and decoding by linear programming (LP) or iterative message-passing (IMP) decoding algorithms. We derive this graph representation by linearizing the ML detection metric, which transforms the equalization problem into a classical decoding problem. We observe that the performance of LP and IMP decoding on this model are very similar in the uncoded case, while IMP decoding significantly outperforms LP decoding when low-density parity-check (LDPC) codes are used. In particular, in the absence of coding, for certain classes of channels, both LP and IMP algorithms always find the exact ML solution using the proposed graph representation, without an exponential complexity in the size of channel memory, even in some two-dimensional ISI channels. However, for some other channel impulse responses, both decoders have non-diminishing probability of failure as SNR increases. In addition to analyti...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Mohammad H. Taghavi, Paul H. Siegel
• Keywords: Classical Decoding Problem, CORR 2007, Education, Graph Representation, ISI Channels