Improved coding techniques for preceded partial-response channels

Abstract

A coset of a convolutional code may be used to generate a zero-run length limited trellis code for a 1-D partial-response channel. The free squared Euclidean distance, d/sub free//sup 2/, at the channel output is lower bounded by the free Hamming distance of the convolutional code. The lower bound suggests the use of a convolutional code with maximal free Hamming distance, d/sub max/(R,N), for given rate R and number of decoder states N. In this paper we present cosets of convolutional codes that generate trellis codes with d/sub free//sup 2/>d/sub max/(R,N) for rates 1/5/spl les/R/spl les/7/9 and (d/sub free//sup 2/=d/sub max/(R,N) for R=13/16,29/32,61/64, The tabulated convolutional codes with R/spl les/7/9 were not optimized for Hamming distance. Instead, a computer search was used to determine cosets of convolutional codes that exploit the memory of the 1-D channel to increase d/sub free//sup 2/ at the channel output. The search was limited by only considering cosets with certain structural properties. The R/spl ges/13/16 codes were obtained using a new construction technique for convolutional codes with free Hamming distance 4. Newly developed bounds on the maximum zero-run lengths of cosets were used to ensure a short maximum run length at the 1-D channel output.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>