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Abstract

Apparatus for generating a (running digital sum) sequence of digital signals X.sub.k and/or a (partial response coded) sequence of digital signals Y.sub.k, K=1, 2, . . . , such that Y.sub.k =X.sub.k .+-.X.sub.k-l, L and integer, in which the Y.sub.x signals are a sequence in a given modulation code. In one aspect, the signals Y.sub.k are chosen to be congruent to coset representatives specified in accordance with a modulation code, a plurality of code constellations are used, and at least one constellation includes both a point with a positive sum of coordinates and one with a negative sum of coordinates. In another aspect, the signals X.sub.k are chosen to be congruent to a sequence of alternate (precoded) coset representatives. In other aspects, the Y.sub.k alphabet signals are evenly spaced, and a selectable, e.g., an optimal, tradeoff between S.sub.x and S.sub.y is made. An N-dimentional modulation code is generated as a sequence of one-dimensional signals. A maximum likelihood sequence estimation decoder reconstructs the estimated running digital sum, and generates a signal whenever the estimated running digital sum is outside a permissible range. In another aspect, the decoder includes a modified maximum likelihood sequence estimator adapted to find MQ partial decoded sequences, where Q is the number of encoder states, and M is an integer.

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