INPoD: In-Network Processing over Sensor Networks based on Code Design

In this paper, we develop a joint network coding (NC)-channel coding error-resilient sensor-network approach that performs in-network processing based on channel code design (INPoD). INPoD represents a major development of an underlying framework for designing code-on-network-graph (CNG). CNG (and hence INPoD) maps variable nodes of low density parity check (LDPC) codes onto sensor nodes, and consequently translates check equations (used in linear algebraic LDPC codes) into in-network processing. INPoD/CNG codes not only improve capacity, but are also resilient to errors in noisy environments. In absence of INPoD, basic CNG employs standard LDPC codes while assuming the underlying sensor network is capable of supporting the degree distribution dictated by these codes. In practice, however, we usually have the network topology pre-determined by the placement of the sensors, and hence we are constrained to map a code onto a given topology. In this paper, we specifically address this problem, and propose the INPoD framework which enables the use of LDPC design tools in the design of CNG for a given sensor network topology. We formulate the design of CNG, as a convex optimization problem, which determines the best codes to be used, given the underlying network connectivity and channel conditions. Specifically, we use
density

evolution
to design degree distributions which controls the performance of the joint NC-channel code CNG. We also give a code construction algorithm, which achieves a designed degree distribution. We show that well-designed INPoD provide gains of 1.5 to 2.5 dB, when compared with the best known erasure codes - LT codes.