Sequence detection based on a variable state trellis for multidimensional ISI channels

Near-optimum sequence detection in channels with intersymbol interference (ISI) is based on the Viterbi algorithm. However, its complexity increases exponentially with the number of taps within the span of the ISI and with the number of symbol levels. We present a low-complexity sequence detection scheme, based on the Viterbi detection algorithm, which is generalized for multidimensional ISI channels in the presence of the predominant signal-dependent noise. The proposed variable state trellis (VST) approach detects and discards in real time states that are unlikely to correspond to the survivor path, thus reducing the complexity of the sequence detection significantly. After analyzing and exploiting a number of criteria (such as a priori reliability information, channel characteristics, and probability of error occurrences among different symbol levels), we propose three approaches to implement the VST scheme. The VST can be applied to any multidimensional ISI channel, including magnetic and optical storage. We compare the performance of the VST and conventional Viterbi algorithms for the multilevel two-dimensional optical storage channel, where media noise is predominant, and show that, with negligible performance loss, the computational complexity is reduced significantly.