P 2 Codes : Pragmatic Trellis Codes Utilizing

QUAL COMM Israel. rror correction codes come in two flavors: block codes and convolutional codes. The most popular method of combining modulation and coding has been termed trellis coded modulation [ l ] (or more simply trellis codes). Pragmatic trellis codes were introduced in a previous IEEE Communications Magazine article [2] whereby the encoders and decoders for trellis codes were obtained by making slight modifications in a readily available convolutional encoder and decoder. In particular, the article described how the Viterbi decoder for the de facto industry and government standard, rate 1/2,64-state, convolutional code could be modified to become the decoder for trellis codes for 8-PSKand 16-PSKmodulation. These pragmatic trellis codes performed almost as well as the best trellis codes of comparable complexity (for an AWGN channel). Indeed, a pragmatic trellis code on a chip has been available for several years for 8-PSK and 16-PSK modulation. Pragmatic codes for PAM and QAM signal constellations were also described [2]. The approach suggested was to treat the QAM constellation as the product of two orthogonal PAM constellations and to code each of these separately. This approach, which was limited to rectangular or square QAM constellations, required quadrupling thenumber of signal points. Since decoding was accomptished by decomposing the twodimensional QAM constellation into two PAM signals, two Viterbi decoders were required. Furthermore, the technique did not apply to the familiar cross constellation. One characteristic of convolutional codes that has been exploited in commercially available products is that a single convolutional code of fixed rate (say rate 1/2) can bepunctured to form a class of higher rate convolutional codes (say rate 2/3,3/4, etc.). In this article, we extend this pragmatic approach to the casewhere the core of the trellis decoder is a Viterbi Decoder for a punctured version of the de facto standard, rate 112 convolutional code. We show that this approach leads to a wide class of high-rate pragmatic punctured (or P2) trellis codes for both PSK and QAM modulation. For PSK modulation, we show that the pragmatic punctured trellis codes lead to more efficient codes than the unpunctured pragmatic trellis codes. For QAM modulation, we demonstrate trellis codes which require only twice the number of signal points, which use only one Viterbi decoder, andwhich apply to rectangular, square or cross constellations. In a recent patent [3] a rate 4/5 pragmatic (but unpunctured) trellis code was described for the 32-QAM cross constellation, which required only twice the number of signal points and which used onlyone Viterbi decoder. Using our P2approach, one is able to obtain almost the same performance as this code but with a higher rate (a rate 9/10) code.