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Delay-constrained asymptotically optimal detection using signal-space partitioning

A signal-space detector estimates the channel input symbol based on the location of the finite-length observation signal in a multi-dimensional signal-space. The decision boundary is formed by a set of hyperplanes. The resulting detector structure consists of linear discriminant functions, threshold detectors, and a Boolean logic function. Our goal is to minimize the number of linear discriminant functions (hyperplanes) with the same or negligible performance loss relative to the maximum likelihood sequence detector. Given all possible fixed-length signal sequences, our procedure finds a minimal set of hyperplanes by which every pair of opposite class signals can be separated by distance no less than the prescribed minimum distance. The proposed methods are applied to practical magnetic recording channels.