2020/04/07 by Touheed Anwar Atif, Atif, Touheed Anwar, Arun Padakandla +3
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.2004.03651
arxiv created 2021/04/29 · arxiv updated 2021/05/03
We consider a scenario wherein two parties Alice and Bob are provided X1n and X2n -- samples that are IID from a PMF PX1 X2. Alice and Bob can communicate to Charles over (noiseless) communication links of rate R1 and R2 respectively. Their goal is to enable Charles generate samples Yn such that the triple (X1n,X2n,Yn) has a PMF that is close, in total variation, to ∏ PX1 X2 Y. In addition, the three parties may posses pairwise shared common randomness at rates C1 and C2. We address the problem of characterizing the set of rate quadruples (R1,R2,C1,C2) for which the above goal can be accomplished. We provide a set of sufficient conditions, i.e. an inner bound to the achievable rate region, and necessary conditions, i.e. an outer bound to the rate region for this three party setup. We provide a joint-typicality based random coding argument involving encoding and decoding operations to perform soft covering and a pertinent relaxation of the PMF requirement for the encoders.