Operational Duality Between Lossy Compression and Channel Coding
The authors explore the duality between lossy compression and channel coding in the operational sense: whether a capacity-achieving encoder-decoder sequence achieves the rate-distortion function of the dual problem when the channel decoder [encoder] is the source compressor [de-compressor, resp.], and vice versa. They show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoder-decoder sequence, or rate-distortion achieving compressor-de-compressor sequence. They show that there exist optimal channel coding [lossy compression] schemes, which fail when used for the dual lossy compression [channel coding resp.] problem.