Multiple description source coding with excess rate

Multiple description source coding concerns situations in which the transmission of the source information is distributed over two channels at rates R₁ and R₂, respectively. When both channels are operative, the decoder receives data at rate R₁ +R₂ which is used to reconstruct the source information with average distortion d₀. If one of the channels breaks down, the receiver has to base its reconstruction solely on the data available at rate either R₁ or R₂, depending on which channel is operative. This results in a higher distortion of either d₁ or d₂, respectively. The region R of all quintuples (R₁,R₂, d₀, d_l, d ₂) has been determined in the so-called Σ`no excess rate´ 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 in which R₁+R₂>R(d₀) is permitted seems difficult. Hence we study here a special case of the excess rate problem