## The Minimax Distortion Redundancy in Noisy Source Coding (2003)

Citations: | 12 - 5 self |

### BibTeX

@MISC{Dembo03theminimax,

author = {Amir Dembo and Tsachy Weissman},

title = {The Minimax Distortion Redundancy in Noisy Source Coding},

year = {2003}

}

### OpenURL

### Abstract

Consider the problem of finite-rate filtering of a discrete memoryless process i#1 based on its noisy observation sequence i#1 , which is the output of a Discrete Memoryless Channel (DMC) whose input is i#1 . When the distribution of the pairs (X i , Z i ), PX,Z , is known, and for a given distortion measure, the solution to this problem is well known to be given by classical rate-distortion theory upon the introduction of a modified distortion measure. In this work we address the case where PX,Z , rather than being completely specified, is only known to belong to some set #. For a fixed encoding rate R we look at the worst case, over all # #, of the di#erence between the expected distortion of a given scheme which is not allowed to depend on the active source # # and the value of the distortion-rate function at R corresponding to the noisy source #. We study the minimum attainable value achievable by any scheme operating at rate R for this worst-case quantity, denoted by D(#, R). Linking between this problem and that of source coding under several distortion measures, we prove a coding theorem for the latter problem and apply it to characterize D(#, R) for the case where all members of # share the same noisy marginal. For the case of a general #, we obtain a single-letter characterization of D(#, R) for the finite-alphabet case. This gives, in particular, a necessary and su#cient condition on the set # for the existence of a coding scheme which is universally optimal for all members of # and characterizes the approximation-estimation tradeo# for statistical modelling of noisy source coding problems. Finally, we obtain D(#, R) in closed form for cases where # consists of distributions on the (channel) input-output pair of a Bernoul...