Exploitable results
The general objective of this project was to find fundamental limits for communication situations and to develop methods and techniques that achieve these limits. The methods were based on mathematical and statistical tools. The project distinguished four different research areas: (i) source coding theory (data compression), (ii) channel coding theory, (iii) network information theory, and (iv) statistical information and communication theory.
In the area of source coding, extensions were given of the context-tree weighting algorithm, such as from binary to nonbinary sources, from finite depth to arbitrary depth tree sources, and the combination of the CTW method with other universal source coding algorithms. Techniques were developed to reduce the complexity of the CTW algorithm. Results were also obtained in the area of successive source and channel coding under fidelity constraints and in tile area of Markov fields defined on two-dimensional lattices.
In channel coding theory, research concentrated on coding for channels with feedback and coding for channels with localized errors. Low rate noiseless feedback strategies were found for AWGN channels. Multiple-repetition feedback strategies for DMC's were discovered and generalized. It was shown that a constant weight code exists which achieves highest rate for detecting localized errors, and that the Hamming bound is asymptotically tight for codes correcting weakly localized errors. Also, upper bounds for the capacity and error exponent of the Poisson channel were derived, based on a new sphere-packing lower bound for the error probability.
In network information theory, bounds were constructed for the E-capacity region of broadcast channel, restricted two-way channel and interference channel. Bounds on the rate-reliabilities-distortions regions for several source networks were derived, such as for multiple descriptions and cascade communication systems with and without secrecy constraints. Coding strategies for and in format ion-theoretical aspects of the two-way channel were also investigated.
In statistical information and communication theory, the asymptotic behavior was investigated of information rates in stationary non-Gaussian channels with weak signal transmission. Exact and asymptotic expressions were found for the information rates in a large class of stationary channels with a random parameter, including channels with additive-multiplicative noise. In filtering theory, tipper and lower bounds were obtained for the mean-square error of the optimal nonlinear filtering of a discrete-time stationary process from the observations. Some bounds were found in terms of information rate. Conditions were found under which error-free filtering is possible. Various results were obtained in the interplay between information theory and statistics, such as on testing hypotheses, identification, signal detection, nonparametric entropy estimation, and information theoretic distribution estimation.
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