Title: On the Binary Lossless Many-Help-One Problem with Independently Degraded Helpers,
Abstract: Although the rate region for the lossless many-help-one problem with
independently degraded helpers is already "solved", its solution is given in
terms of a convex closure over a set of auxiliary random variables. Thus, for
any such a problem in particular, an optimization over the set of auxiliary
random variables is required to truly solve the rate region. Providing the
solution is surprisingly difficult even for an example as basic as binary
sources. In this work, we derive a simple and tight inner bound on the rate
region's lower boundary for the lossless many-help-one problem with
independently degraded helpers when specialized to sources that are binary,
uniformly distributed, and interrelated through symmetric channels. This
scenario finds important applications in emerging cooperative communication
schemes in which the direct-link transmission is assisted via multiple lossy
relaying links. Numerical results indicate that the derived inner bound proves
increasingly tight as the helpers become more degraded.