A randomized covering-packing duality between source and channel coding

Given a general channel b over which the uniform X source, denoted by U , is directly communicated within distortion D. The source U puts uniform distribution on all sequences with type precisely pX as compared with the i.i.d. X source which puts ‘most of’ its mass on sequences with type ‘close to’ pX . A randomized covering-packing duality is established between source-coding and channel-coding by considering the source-coding problem (covering problem) of coding the source U within distortion D and the channel coding problem (packing problem) of reliable communication over b, thus leading to a proof of C ≥ RU (D) where C is the capacity of b and RU (D) is the rate-distortion function of U . This also leads to an operational view of source-channel separation for communication with a fidelity criterion.