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The computation and bounding of rate-distortion functions

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1 Author(s)

Methods are given for the numerical computation of Shannon's rate-distortion function R(D) for certain memoryless message sources. It is first assumed that U , the set of possible message-source outputs, and V , the set of possible destination symbols, are countable. The computation of R(D) for this case is reduced to a minimization problem in which the variables are the destination-symbol probabilities. For arbitrary U and V , upper and lower bounds on R(D) are derived by partitioning U and V each into a countable collection of disjoint subsets and employing the results derived previously for the case of countable U and V . Conditions are then discussed under which these bounds can be made arbitrarily close to each other by choosing sufficiently fine partitions of U and V . Two examples are included to illustrate the results in detail.

Published in:

IEEE Transactions on Information Theory  (Volume:15 ,  Issue: 5 )