Multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels. This paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed. A compact model is developed for the multiple-input multiple-output (MIMO) dispersive spatially selective wireless communication channel. The multivariate information capacity is analyzed. For high signal-to-noise ratio (SNR) conditions, the MIMO channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components, the number of input antennas, or the number of output antennas. This desirable result is contrasted with the lower capacity slope of the well-studied case with multiple antennas at only one side of the radio link. A spatio-temporal vector-coding (STVC) communication structure is suggested as a means for achieving MIMO channel capacity. The complexity of STVC motivates a more practical reduced-complexity discrete matrix multitone (DMMT) space--frequency coding approach. Both of these structures are shown to be asymptotically optimum. An adaptive-lattice trellis-coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the DMMT channel. Experimental examples that support the theoretical results are presented. Index Terms---Adaptive arrays, adaptive coding, adaptive modulation, antenna arrays, broad-band communication, channel coding, digital modulation, information rates, MIMO systems, multipath channels. I.

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.

It is shown that any point in the capacity region of a Gaussian multiple-access channel is achievable by single-user coding without requiring synchronization among users, provided that each user “splits” data and signal into two parts. Based on this result, a new multiple-access technique called rate-splitting multiple accessing (RSMA) is proposed. RSMA is a code-division multiple-access scheme for the M-user Gaussian multiple-access channel for which the effort of finding the codes for the M users, of encoding, and of decoding is that of at most 2M - 1 independent point-to-point Gaussian channels. The effects of bursty sources, multipath fading, and inter-cell interference are discussed and directions for further research are indicated.

Abstract — General random coding theorems for lattices are derived from the Minkowski–Hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out. A new version of the Minkowski–Hlawka theorem itself is obtained as the limit, for p!1,ofasimple lemma for linear codes over GF (p) used with p-level amplitude modulation. The relation between the combinatorial packing of solid bodies and the information-theoretic “soft packing ” with arbitrarily small, but positive, overlap is illuminated. The “softpacking” results are new. When specialized to the additive white Gaussian noise channel, they reduce to (a version of) the de Buda–Poltyrev result that spherically shaped lattice codes and adecoder that is unaware of the shaping can achieve the rate 1=2 log2 (P=N).

The role of low density parity check principles in the design of group codes for coded modulation is examined. In this context, the structure of linear codes over certain rings Zm and Gm is discussed, and LDPC codes over these ring structures are designed.

Abstract — A length � group code over a group q is a subgroup of q � under component-wise group operation. Group codes over dihedral groups hw, with Pw elements, that are two-level constructible using a binary code and a code over w residue class integer ring modulo w, as component codes are studied for arbitrary w. A set of necessary and sufficient conditions on the component codes for the two-level construction to result in a group code over hw are obtained. The conditions differ for w odd and even. Using two-level group codes over hw as label codes, performance of block-coded modulation scheme is discussed under all possible matched labelings of Pw-APSK and Pw-SPSK (asymmetric and symmetric PSK) signal sets in terms of the minimum squared Euclidean distance. Matched labelings that lead to Automorphic Euclidean Distance Equivalent codes are identified. It is shown that depending upon the ratio of Hamming distances of the component codes some labelings perform better than other. The best labeling is identified under a set of restrictive conditions. Finally, conditions on the component codes for phase rotational invariance properties of the signal space codes are discussed. Index Terms—Coded modulation, dihedral groups, group codes, multilevel codes. I.

. Generalized Hamming weight hierarchies and permutation-optimal trellis decoders are found for several extremal self-dual codes. The latter problem involves finding chains of subcodes that allow construction of a uniformly efficient permutation. The task of finding such chains of subcodes is shown to be substantially simplifiable in the case of self-dual codes in general, and is particularly straightforward when certain subcodes meet the Griesmer bound with equality. These results are used to characterize the permutation-optimal trellises and generalized Hamming weights for all [32; 16;8] binary self-dual codes and for several other codes. The number of uniformly efficient permutations for the [24; 12;8]Golay code, and a lower bound on the number for the [48; 24;12] quadratic residue code, are found. Keywords: Chain condition, Conway-Pless codes, double chain condition, generalized Hamming weights, unique codes. 1. Introduction Representations of block codes by trellises allow comput...

Abstract — This paper develops coding and signal processing approaches for a novel optical recording channel that arises from electron-trapping phosphor materials. The recording medium allows multiple reads and writes, and one important feature is that the read process serves to erase the disk. This feature would enable vendors of prerecorded video to provide customers with one-time services. For applications where this feature is not desirable, the data can be immediately rewritten. From a communications viewpoint, the most important feature of this new channel is that, subject to a peak constraint, it supports a continuum of recording levels. The combination of read and write processes creates a partial-response channel, and the ability to write a continuum of levels makes it possible to employ precoding techniques, such as the one developed by Tomlinson (1971) and by Miyakawa and Harashima (1969). This is fundamentally different from magnetic data storage, where the read/write process creates a partial-response channel but where it is only possible to write two levels at the input to that channel. This paper shows that the use of precoding and coset codes can significantly improve upon the recording densities (and recording rates) that can be achieved by using w-ary run length constrained codes to eliminate intersymbol interference (ISI) at the output of the read/write process. The approach presented here is applicable to any optical recording channel that supports a continuum of recording levels. Index Terms—Electron-trapping optical memory, optical data storage, partial-response channels, Tomlinson–Harashima precoding. I.

In a recent paper, it is shown that if Pearl's belief propagation algorithm is applied to the Bayesian belief network of a turbo code, the turbo decoding algorithm immediately results. From this perspective, it is recognized that the turbo coding structure imposes unnecessary differentiation on the parity checks and the turbo decoding algorithm specifies a seemingly arbitrary sequential activation order for the network. In this paper, a class of high-rate systematic block codes based on pseudo-random low-density generator matrices are proposed as a generalization of the turbo codes in which the parity bits are treated uniformly. These codes can be encoded and decoded in linear time with a parallel distributive decoding algorithm derived from the belief propagation algorithm. We also apply these codes to M-ary modulations using multilevel coding techniques to achieve higher spectral efficiency. In all cases, we have constructed systems with flexible error protection capability and perfo...

Abstract — Low density lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional Euclidean space as a linear transformation of a corresponding integer message vector b, i.e., x = Gb, where H = G −1 is restricted to be sparse. The fact that H is sparse is utilized to develop a lineartime iterative decoding scheme which attains, as demonstrated by simulations, good error performance within ∼ 0.5dB from capacity at block length of n = 100, 000 symbols. The paper also discusses convergence results and implementation considerations. I.