Multilevel diversity coding with symmetrical connectivity

Multilevel diversity coding was recently introduced by Roche (1992) and Yeung (1995). In a multilevel diversity coding system, the decoders are partitioned into multiple levels. The reconstructions of the source by decoders within the same level are identical and are subject to the same distortion criterion. Previously, a class of problems in multilevel diversity coding was suggested. In this paper we consider one such problem with symmetrical connectivity between the encoders and decoders. In this problem, there are three encoders and seven decoders. The source {X_k} is an independent and identically distributed (i.i.d.) process. The seven decoders belong to three levels: decoders 1, 2, and 3 belong to level 1; decoders 4, 5, and 6 belong to level 2; and decoder 7 belongs to level 3. Note that each level i decoder has access to i encoders, and {(X¯_i)_k} is the reproduction of {X_k} by a level i decoder. We are interested in finding the trade-off between the rates of the encoders and the distortions of the reconstructions of the source by the decoders