Trellis modulation

Abstract: A suboptimal trellis coding approach based on the concept of combining a good convolutional code and bit interleavers is presented. The aim is to improve the reliability of digital radio communication over a fading channel. It is shown that over a Rayleigh channel and for a fixed code complexity the proposed system is superior to the baseline system. Its performance is analyzed using the generalized R/sub o/ and the upper bound on the bit error rate. The results suggest that on a Rayleigh channel, the standard trellis codes may not be the correct approach for improving the reliability of the communication channel. The discussion is restricted to a rate 2/3 coded system with 8-PSK modulation. >

Abstract: We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB.

Abstract: rellis-Coded Modulation (TCM) has evolved over the past decade as a combined coding and modulation technique for digital transmission over band-limited channels. Its main attraction comes from the fact that it allows the achievement of significant coding gains over conventional uncoded multilevel modulation without compromising bandwidth efficiency. T h e first TCM schemes were proposed in 1976 [I]. Following a more detailed publication [2] in 1982, an explosion of research and actual implementations of TCM took place, to the point where today there is a good understanding of the theory and capabilities of TCM methods. In Part 1 of this two-part article, an introduction into TCM is given. T h e reasons for the development of TCM are reviewed, and examples of simple TCM schemes are discussed. Part I1 [I51 provides further insight into code design and performance, and addresses. recent advances in TCM. TCM schemes employ redundant nonbinary modulation in combination with a finite-state encoder which governs the selection of modulation signals to generate coded signal sequences. In the receiver, the noisy signals are decoded by a soft-decision maximum-likelihood sequence decoder. Simple four-state TCM schemes can improve. the robustness of digital transmission against additive noise by 3 dB, compared to conventional , uncoded modulation. With more complex TCM schemes, the coding gain can reach 6 dB or more. These gains are obtained without bandwidth expansion or reduction of the effective information rate as required by traditional error-correction schemes. Shannon's information theory predicted the existence of coded modulation schemes with these characteristics more than three decades ago. T h e development of effective TCM techniques and today's signal-processing technology now allow these ,gains to be obtained in practice. Signal waveforms representing information sequences ~ are most impervious to noise-induced detection errors if they are very different from each other. Mathematically, this translates into therequirement that signal sequences should have large distance in Euclidean signal space. ~ T h e essential new concept of TCM that led to the afore-1 mentioned gains was to use signal-set expansion to I provide redundancy for coding, and to design coding and ' signal-mapping functions jointly so as to maximize ~ directly the \" free distance \" (minimum Euclidean distance) between coded signal sequences. This allowed the construction of modulation codes whose free distance significantly exceeded the minimum distance between uncoded modulation signals, at the same information rate, bandwidth, and signal power. The term \" …

Abstract: I the,art in trellis-coded modulation (TCM) is given for the more interested reader. First, the general structure of TCM schemes and the principles of code construction are reviewed. Next, the effects of carrier-phase offset in carrier-modulated TCM systems are discussed. The topic i s important, since TCM schemes turn out to be more sensitive to phase offset than uncoded modulation systems. Also, TCM schemes are generally not phase invariant to the same extent as their signal sets. Finally, recent advances in TCM schemes that use signal sets defined in more than two dimensions are described, and other work related to trellis-coded modulation is mentioned. The best codes currently known for one-, two-, four-, and eight-dimensional signal sets are given in an Appendix. T h e trellis structure of the early hand-designed TCM schemes and the heuristic rules used to assign signals to trellis transitions suggested that TCM schemes should have an interpretation in terms of convolutional codes with a special signal mapping. This mapping should be based on grouping signals into subsets with large distance between the subset signals. Attempts to explain TCM schemes in this manner led to the general structure of TCM encoders/modulators depicted in Fig. 1. According to this figure, TCM signals are generated as follows: When m bits are to be transmitted per encoder/modulator operation, m 5 m bits are expanded by a rate-rYd(m-t 1) binary convolutional encoder into rii-t 1 coded bits. These bits are used to select one of 2' \" + I subsets of a redundant 2'11+1-ary signal set. The remaining mm uncoded bits determine which of the 2 \" '-' \" signals in this subset is to be transmitted. The concept of set partitioning is of central significance for TCM schemes. Figure 2 shows this concept for a 32-CROSS signal set [ 11, a signal set of lattice type \" Z2 \". Generally, the notation \" Zk \" is used to denote an infinite \" lattice \" of points in k-dimensional space with integer coordinates. Lattice-type signal sets are finite subsets of lattice points, which are centered around the origin and have a minimum spacing of A,. Set partitioning divides a signal set successively into smaller subsets with maximally increasing smallest two-way. The partitioning is repeated iii 4-1 times until A,,+, is equal to or greater than the desired free distance of the TCM scheme to be designed. T h e finally …