About priority encoding transmission

Recently, (PET) for sending hierarchically organized messages over lossy pa cket-based computer networks [1], In a PET system, each symbol in the messa ge is assigned a priority which determines the minimal number of codeword s ymbols that is required to recover that symbol. This note revisits the PET approach using tools from network information theory. We first outline that priority encoding transmission is intimately related with the broadcast er asure channel with degraded message set, Using the information spectrum app roach, we provide an informational characterization of the capacity region of general broadcast channels with degraded message set, We show that the P ET inequality has an information-theoretical counterpart. The inequality de fining the capacity region of the broadcast erasure channel with degraded m essage sets. Hence the PET approach which consists in time-sharing and inte rleaving classical erasure-resilient codes achieves the capacity region of this channel. Moreover, we show that the PET approach may achieve the spher e packing exponents. Finally, we observe that on some simple nonstationary broadcast channels, time-sharing may be outperformed. The impact of memory on the optimality of the PET approach remains elusive.