Almost Lossless Onion Peeling Data Compression

This work considers almost lossless onion peeling data compression. In onion peeling data compression, as in Slepian-Wolf data compression, multiple transmitters independently encode their respective sources and transmit their descriptions to a shared decoder. Onion peeling codes differ from Slepian-Wolf codes in that the onion peeling decoder must sequentially decode the individual sources rather than making a single joint decoding decision. This work considers an almost lossless two-stage code. The main result shows that when the first source is coded by a near-optimal code for a given first-stage error constraint, the conditional entropy rate of the second source, given this imperfect reconstruction, can vary within a gap that does not vanish when the blocklength grows without bound. It is also shown that the lower bound for the second-stage conditional entropy rate can be achieved using a classic random binning code in the first stage.