  Inter-symbol interference (ISI) channels with data dependent Gauss Markov
noise have been used to model read channels in magnetic recording and other
data storage systems. The Viterbi algorithm can be adapted for performing
maximum likelihood sequence detection in such channels. However, the problem of
finding an analytical upper bound on the bit error rate of the Viterbi detector
in this case has not been fully investigated. Current techniques rely on an
exhaustive enumeration of short error events and determine the BER using a
union bound. In this work, we consider a subset of the class of ISI channels
with data dependent Gauss-Markov noise. We derive an upper bound on the
pairwise error probability (PEP) between the transmitted bit sequence and the
decoded bit sequence that can be expressed as a product of functions depending
on current and previous states in the (incorrect) decoded sequence and the
(correct) transmitted sequence. In general, the PEP is asymmetric. The average
BER over all possible bit sequences is then determined using a pairwise state
diagram. Simulations results which corroborate the analysis of upper bound,
demonstrate that analytic bound on BER is tight in high SNR regime. In the high
SNR regime, our proposed upper bound obviates the need for computationally
expensive simulation.
