Exact repair problems with multiple sources

We consider a new variant of the exact repair distributed storage problem, the multi-source exact repair problem, wherein the reconstruction decoders are each only required to provide a subset of the source variables. To best illustrate the idea, we generalize the (n, k, d) = (3, 2, 2) exact repair distributed storage problem to the multisource case. When every decoder demands all source variables, the rate region of the (3, 2, 2) exact repair problem is known to be same as that of the (3, 2, 2) functional repair problem, while the rate region for (3, 2, 2) case with multiple sources is unknown. We find achievable rate regions for vector binary and scalar binary codes via an automated approach.