Stable Source Coding

A source encoder is stable if a small change in the source sequence (e.g., changing a few symbols) results in a small (or bounded) change in the output codeword. By this definition, the common technique of random binning is unstable; because the mapping is random, two nearly identical source sequences can be assigned to completely unrelated bin indices. We study compression rates of stable lossless source codes. Using combinatorial arguments, we derive information-theoretic limits on the achievable rate as a function of the stability parameters.