Abstracts of Forthcoming Manuscripts Universal Space-Time Codes From Demultiplexed Trellis Codes
Cenk Kose, Richard D. Wesel, Sasan Nikneshan, Amir Keyvan Khandani · 2006
In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual infor- mation (MI) is above the transmitted rate. This paper presents 2-D trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes are found by an exhaustive search that guarantees consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or in some cases, superior frame-error rate and bit-error rate performance under quasi-static Rayleigh fading to trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh fading scenario. Abstract—This paper describes a new approach to fixed-rate entropy- constrained vector quantization (FEVQ) for stationary memoryless sources where the structure of codewords are derived from a variable-length scalar quantizer. We formulate the quantization search operation as a zero-one integer optimization problem, and show that the resulting integer program can be closely approximated by solving a simple linear program. The re- sult is a Lagrange formulation which adjoins the constraint on the entropy (codeword length) to the distortion. Unlike the previously known methods with a fixed Lagrange multiplier, we use an iterative algorithm to optimize the underlying objective function while updating the Lagrange multiplier until the constraint on the overall rate is satisfied. The key feature of the new method is the substantial reduction in the number of iterations, in compar- ison with previous related methods. In order to achieve some packing gain, we combine the process of trellis-coded quantization with that of FEVQ. This results in an iterative application of the Viterbi algorithm on the un- derlying trellis for selecting the Lagrange multiplier. Numerical results are presented which demonstrate substantial improvement in comparison with the alternative methods reported in the literature.