Converse and duality results for combinatorial source-channel coding in binary Hamming spaces

This article continues the recent investigation of combinatorial joint source-channel coding. For the special case of a binary source and channel subject to distortion measured by Hamming distance, the lower (converse) bounds on achievable source distortion are improved for all values of channel noise. Operational duality between coding with bandwidth expansion factors ρ and 1 over ρ is established. Although the exact value of the asymptotic noise-distortion tradeoff curve is unknown (except at ρ = 1), some initial results on inter-relations between these curves for different values of ρ are shown and lead to statements about monotonicity and continuity in ρ.