Multiple description source coding with no excess marginal rate

Multiple description source coding concerns situations in which the transmission of the source information is distributed over two data streams at rates R₁ and R₂, respectively. When both data streams are received, the decoder uses the combined data at rate R₁+R₂ to reconstruct the source information with average distortion d₀. If a communication breakdown prevents one of the data streams from reaching the receiver, the decoder has to base its reconstruction solely on the available data at rate either R₁ or R₂. This results in a higher distortion of either d₁ or d₂, respectively. The region ℛ of all achievable quintuples (R₁, R₂, d₀, d₁, d₂) has been determined in the so-called “no excess rate” sum case defined by imposing the requirement R₁+R₂=R(d₀), where R(·) is the rate-distortion function of the source. The case with excess rate sum, characterized by R₁+R₂>R(d₀), is challenging. We study in this paper a special case of it in which the requirements R_t=R(d_t), t=1, 2, are imposed; we refer to this as the “no excess marginal rate” case. The lower and upper bounds on d₀ we obtain are separated by only a tiny gap when evaluated for a binary equiprobable source and the Hamming distortion measure