The optimum combination of block codes and receivers for arbitrary channels

A determination is made of the combinations of transmitted block codewords and matching receiver filters that maximize the signal-to-noise ratio at the detector with arbitrary channel impulse response and arbitrary noise spectrum. This permits representing the channel as a set of parallel, uncoupled subchannels with uncorrelated noise; the representation is used to calculate the capacity of an arbitrary block coded, time discrete channel. It is shown that substantial coding gains, compared to symbol-by-symbol processing, can be achieved. The block code used can be concatenated with trellis-coded modulation so that the two coding gains are additive.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>