Practical Universal Decoding for Combined Routing and Compression in Network Coding

Minimum-entropy decoding is a universal decoding algorithm used in decoding block compression of discrete memoryless sources as their multiterminal counterparts, such as the Slepian-Wolf problem. It has recently been shown that such an algorithm can be applied for combined distributed compression and distributed routing in a randomized distributed network coding framework. The ‘method of types’ shows that there exist linear codes that when applied with such an algorithm, can attain the same error exponent as that of a maximum-likelihood decoder. Owing to the algorithm being generally NP-hard, the traditional rationale for discussing this technique has been mostly theoretical pursuit. Here we discuss practical approximation algorithms to minimum-entropy decoding by using ideas from linear programming. We exploit two main facts. First, the ‘method of types’ shows that that the number of distinct types is polynomial in the block length n. Second, recent results in the optimization literature have illustrated polytope projection algorithms whose complexity is a function of the number of vertices of the polytope projection. Combining these two ideas, we leverage recent results on linear programming as a relaxation for error correcting codes to construct polynomial complexity algorithms for this setting.