Maximal Recovery Network Coding under Topology Constraint

Recent advances have shown that channel codes can be mapped onto networks to realize efficient Network Coding (NC); this has led to the emergence of Code-on-Network-Graphs (CNG). Traditional CNG approaches (e.g Decentralized Erasure Codes) focus on a generating a sequence of encoded symbols from a given input source (of size K), such that the original symbols can be recovered from any subset of the encoded symbols of size equal to or slightly larger than K. However in all cases the number of source symbols recovered falls rapidly if the number of encoded symbols received falls below K. In this paper we determine the CNG code-ensembles (under statistical toplogy constraint) which result in maximal recovery of WSN source data (for different erasure-rates), thereby minimizing the deterioration in data recovery. We also perform fixed point stability analysis on the underlying LDPC code ensemble. We then propose a distributed algorithm for generating a sequence of encoded symbols adhering to the designed code ensemble. Optimal solutions for a sensor network with 1000 nodes is determined using the Differential Evolution algorithm, and the solution sensitivity to variance in number of sensor nodes and node-interconnectivity is evaluated.