On the Many-Help-One Problem with Independently Degraded Helpers

This work provides new results for the separated encoding of correlated discrete memoryless sources. We address the scenario where an arbitrary number of auxiliary sources (a.k.a. helpers) are supposed to help decode a single primary source errorless. The rate-distortion analysis of such a system establishes the so-called many-help-one problem. We focus on the case in which the auxiliary sources are conditionally independent, given the primary source. We provide an inner and an outer bound of the ratedistortion region for what we call the strong many-help-one problem, where the auxiliary sources must be also recovered under certain distortion constraints. Furthermore, based on known results from the CEO problem we provide the admissible rate region for what we call the weak many-help-one problem, where the auxiliary sources do not need to be recovered serving merely as side information to help recover the primary source. Both scenarios find important application to emerging cooperative techniques in which a direct-link communication is assisted by multiple lossy relaying-link transmissions. Motivated by this application, we specialize the referred scenarios to binary sources and the Hamming distortion measure. Remarkably, we show that for the weak many-help-one problem the independent decoding of the auxiliary sources can achieve optimal performance. Index Terms Admissable rate region, correlated sources, distributed source coding, many-help-one problem, rate-distortion region.