Matched spectral null trellis codes for partial response channels II. High rate codes with simplified viterbi detectors

Abstract

Summary form only given. A new method is proposed for the design of high-rate binary trellis codes for noisy partial response channels with maximum likelihood detection, with emphasis on channels of interest in data transmission and storage. The channels considered have transfer polynomials of the form (1 - D)N (1 + D)M, including dicode (N = 1, M = 0), class 1 (N = 0, M = 1), class 2 (N = 0, M = 2), class 4 (N = 1, M = 1), and extended class 4 (N = 1, M = 2). The method hinges upon the principle of matched spectral nulls: the code spectrum and its derivatives are designed to have nulls precisely at those frequencies where the channel transfer function has a null. Euclidean distance properties of spectral null constraints are derived, along with the representation of the sequences by means of canonical state diagrams. Reduced-complexity Viterbi detectors are defined for these codes, with trellis structures derived from the canonical state diagrams. The codes are shown to preclude quasi-catastrophic error events in the trellis; thus, the simplified Viterbi detectors achieve coding gains that nearly match the performance of full maximum-likelihood detectors.