In this paper, we study the performance of different graph-based error correcting codes over Gilbert-Elliott channels. We propose a hybrid coding scheme in which each code bit is checked by both a parity check and a Hamming code. A hybrid code can be represented by a code-to-code graph, which can be used to optimize the code. Asymptotic minimum distance properties of the hybrid code are derived and it is shown that the expected minimum distance of the hybrid code increases linearly with respect to the code length. Simulation results show that for a typical Gilbert-Elliott channel, hybrid codes can outperform regular low-density parity check (LDPC) codes by more than an order of magnitude in terms of bit error rate.
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