Multilevel ternary line codes with trellis structure

Abstract

A combination of the two coding techniques given by Imai and Hirakawa (1977) and Pottie and Taylor (1989) is applied to the ternary (+, 0, -) line-code design problem. New ternary coding systems are obtained with reduced decoding complexity and improved error performance, compared with those obtained by the classical Ungerboeck's trellis-coding approach. The decoding complexity for high coding rates is reduced by the proper choice of the punctured convolutional component codes for each partitioning level. A spectral null at zero frequency is obtained by the use of a halfrate unit-memory convolutional encoder at the last partitioning level which selects line codewords with opposite disparities in an alternated fashion so that the running-digital-sum values vary in a finite interval. The effects of the path multiplicity are evaluated by upper bounding the bit error probabilities based on the union-bound approach.