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Berger, T.

Publications and source records attributed to Berger, T..

Tree encoding of Gaussian sources

Tree codes are known to be capable of performing arbitrarily close to the rate-distortion function for any memoryless source and single-letter fidelity criterion. Tree coding and tree search strategies are investigated for the discrete-time memoryless Gaussian source encoded for a signal-power-to-mean-squared-error ratio of about 30 dB (about 5 binary digits per source output). Also, a theoretical lower bound on average search effort is derived. Two code search strategies (the Viterbi algorithm and the stack algorithm) were simulated in assembly language on a large digital computer. After suitable modifications, both strategies yielded encoding with a signal-to-distortion ratio about 1 dB below the limit set by the rate-distortion function. Although this performance is better than that of any previously known instrumentable scheme, it unfortunately requires search computation of the order of 100,000 machine cycles per source output encoded.

Dick, R. J.

Permutation codes for sources.

Source encoding techniques based on permutation codes are investigated. For a broad class of distortion measures it is shown that optimum encoding of a source permutation code is easy to instrument even for very long block lengths. Also, the nonparametric nature of permutation encoding is well suited to situations involving unknown source statistics. For the squared-error distortion measure a procedure for generating good permutation codes of a given rate and block length is described. The performance of such codes for a memoryless Gaussian source is compared both with the rate-distortion function bound and with the performance of various quantization schemes. The comparison reveals that permutation codes are asymptotically ideal for small rates and perform as well as the best entropy-coded quantizers presently known for intermediate rates. They can be made to compare favorably at high rates, too, provided the coding delay associated with extremely long block lengths is tolerable.

Berger, T.