| Consider a communication scenario in which a source is encoded into N packets, at most T of which may be arbitrarily altered by an omniscient adversary. Unlike prior work in coding theory which seeks to optimize only the worst-case performance of the code, in this work, codes are designed to enable the decoder to reproduce the source subject to a certain distortion constraint when there are no packets errors, subject to a less stringent distortion constraint when there is one error, etc. The topic of this thesis is to find the trade-off between rate and distortion in such communication scenarios.;A code design based on the Polytope codes is introduced for the binary source with erasure distortion measure and is also proven to have partial optimality property. Moreover, for the point-to-point scenario (N = 1 and T = 1), both inner bounds and outer bounds are derived for discrete sources with finite alphabet with general distortion measure. For the binary source with Hamming distortion, these two bounds are proven to be the same.;For a Gaussian source with a mean-square error distortion, it is shown that a natural design based on MDS codes is not order-optimal in the rate as the distortion constraint tends to zero, but a hybrid scheme that involves a form of uncoded transmission is. We derive an outer bound which has a constant gap with the inner bound naturally generated by the codes we design, thus fully characterizing the Rate-Distortion region. |
