Modified Viterbi algorithm for efficient optimal decoding of pragmatic-punctured trellis-coded modulation

Abstract

In classic trellis-coded modulation (TCM) signal constellations of twice the cardinality are applied when compared to an uncoded transmission enabling transmission of one bit of redundancy per PAM-symbol, i.e., rates of K when 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K+1</sup> denotes the cardinality of the signal constellation. In order to support different rates, multi-dimensional (i.e., D-dimensional) constellations had been proposed by means of combining subsequent one- or two-dimensional modulation steps, resulting in TCM-schemes with <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> bit redundancy per real dimension. In contrast we propose in this paper to perform rate adjustment for TCM by means of puncturing the convolutional code (CC) on which a TCM-scheme is based on. Even though TCM is a topic that has received a lot of attention over the years, the problem of optimal and complexity efficient decoding of a punctured convolutional encoder in TCM was not yet solved without some drawbacks. Here we overcome this problems by usage of a time-variant trellis following the nontrivial mapping of the output symbols of the CC to signal points. For this, some modifications of the Viterbi-decoder are presented and good generator polynomials for the CC as well as corresponding puncturing schemes are given. The proposed approach offers several decisive advantages over multidimensional TCM w.r.t. flexibility and complexity.