Lower bound for ML sequence detection in ISI channels with Gauss Markov noise

In past, inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been prevalently used to model read channels for magnetic recording and other data storage systems. The maximum likelihood sequence detection in such channels is solved using the Viterbi algorithm. However, the problem of finding an analytical lower bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. Current techniques do not give the tight lower bound as the bound computation involves only minimum-length error events. In this work, we consider a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive a lower bound on the pairwise error probability (PEP) between the correct bit sequence and the estimated bit sequence that can be expressed as a product of functions depending on current and previous states of the correct and the estimated sequence. In this case, the PEP is asymmetric which precludes the usage of error state diagram method for the bound computation. We present a method of finding a lower bound on the BER through constructing a product trellis. Simulations results corroborate the analysis of the lower bound and demonstrate that the analytic lower bound on BER is tight in a high SNR regime.