We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders.

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Space-time codes for high data rate wireless communication: performance criterion and code construction

We propose a variable-rate and variable-power MQAM modulation scheme for high-speed data transmission over fading channels. We first review results for the Shannon capacity of fading channels with channel side information, where capacity is achieved using adaptive transmission techniques. We then derive the spectral efficiency of our proposed modulation. We show that there is a constant power gap between the spectral efficiency of our proposed technique and the channel capacity, and this gap is a simple function of the required bit-error rate (BER). In addition, using just five or six different signal constellations, we achieve within 1-2 dB of the maximum efficiency using unrestricted constellation sets. We compute the rate at which the transmitter needs to update its power and rate as a function of the channel Doppler frequency for these constellation sets. We also obtain the exact efficiency loss for smaller constellation sets, which may be required if the transmitter adaptation rate is constrained by hardware limitations. Our modulation scheme exhibits a 5-10-dB power gain relative to variable-power fixed-rate transmission, and up to 20 dB of gain relative to nonadaptive transmission. We also determine the effect of channel estimation error and delay on the BER performance of our adaptive scheme. We conclude with a discussion of coding techniques and the relationship between our proposed modulation and Shannon capacity.

Variable-rate variable-power MQAM for fading channels

Space-time codes (STC) are a class of signaling techniques, offering coding and diversity gains along with improved spectral efficiency. These codes exploit both the spatial and the temporal diversity of the wireless link by combining the design of the error correction code, modulation scheme and array processing. STC are well suited for improving the downlink performance, which is the bottleneck in asymmetric applications such as downstream Internet. Three original contributions to the area of STC are presented in this dissertation. First, the development of analytic tools that determine the fundamental limits on the performance of STC in a variety of channel conditions. For trellis-type STC, transfer function based techniques are applied to derive performance bounds over Rayleigh, Rician and correlated fading environments. For block-type STC, an analytic framework that supports various complex orthogonal designs with arbitrary signal cardinalities and array configurations is developed. In the second part of the dissertation, the Virginia Tech Space-Time Advanced Radio (VT-STAR) is designed, introducing a multi-antenna hardware laboratory test bed, which facilitates characterization of the multiple-input multiple-output (MIMO) channel and validation of various space-time approaches. In the third part of the dissertation, two novel space-time architectures paired with iterative processing principles are proposed. The first scheme extends the suitability of STC to outdoor wireless communications by employing iterative equalization/decoding for time dispersive channels and the second scheme employs iterative interference cancellation/decoding to solve the error propagation problem of Bell-Labs Layered Space-Time Architecture (BLAST). Results show that remarkable energy and spectral efficiencies are achievable by combining concepts drawn from space-time coding, multiuser detection, array processing and iterative decoding.

Space-Time Codes for High Data Rate Wireless Communications

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

/pdf/fading-channels-information-theoretic-and-communications-2ipqbail97.pdf

Fading channels: information-theoretic and communications aspects

We address the problem of compressing correlated distributed sources, i.e., correlated sources which are not co-located or which cannot cooperate to directly exploit their correlation. We consider the related problem of compressing a source which is correlated with another source that is available only at the decoder. This problem has been studied in the information theory literature under the name of the Slepian-Wolf (1973) source coding problem for the lossless coding case, and as "rate-distortion with side information" for the lossy coding case. We provide a constructive practical framework based on algebraic trellis codes dubbed as DIstributed Source Coding Using Syndromes (DISCUS), that can be applicable in a variety of settings. Simulation results are presented for source coding of independent and identically distributed (i.i.d.) Gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded. Our results reveal the promise of this approach: using trellis-based quantization and coset construction, the performance of the proposed approach is 2-5 dB from the Wyner-Ziv (1976) bound.

Distributed source coding using syndromes (DISCUS): design and construction

A signal space code C is defined as geometrically uniform if, for any two code sequences in C, there exists an isometry that maps one sequence into the other while leaving the code C invariant. Geometrical uniformity, a strong kind of symmetry, implies such properties as a) the distance profiles from code sequences in C to all other code sequences are all the same, and b) all Voronoi regions of code sequences in C have the same shape. It is stronger than Ungerboeck Zehavi-Wolf symmetry or Calderbank-Sloane regularity. Nonetheless, most known good classes of signal space codes are shown to be generalized coset codes, and therefore geometrically uniform, including (a) lattice-type trellis codes based on lattice partitions Lambda / Lambda ' such that Z/sup N// Lambda / Lambda '/4Z/sup N/ is a lattice partition chain, and (b) phase-shift-keying (PSK)-type trellis codes based on up to four-way partitions of a 2/sup n/-PSK signal set. >

Geometrically uniform codes

The author discusses trellis shaping, a method of selecting a minimum-weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code C/sub s/. Shaping gains on the order of 1 dB may be obtained with simple four-state shaping codes and with moderate constellation expansion. The shaping gains obtained with more complicated codes approach the ultimate shaping gain of 1.53 dB. With a feedback-free syndrome-former for C/sub s/, transmitted data can be recovered without catastrophic error propagation. Constellation expansion and peak-to-average energy ratio may be effectively limited by peak constraints. With lattice-theoretic constellations, the shaping operation may be characterized as a decoding of an initial sequence in a channel trellis code by a minimum-distance decoder for a shaping trellis code based on the shaping convolutional code, and the set of possible transmitted sequences is then the set of code sequences in the channel trellis code that lie in the Voronoi region of the trellis shaping code. >

Trellis shaping

Under certain mild conditions, the minimum Hamming distance D of an (N, K, D) group code C over a non-abelian group G is bounded by D N/2. Consequently, there exists no (N, K, N-K+1) group code C over an non-abelian group G if 1 >

Jr. G.D. Forney

Papers

Geometrically uniform codes

Trellis shaping

On the Hamming distance properties of group codes