Energy Minimization With Network Coding via Latin Hypercubes

Network coding is mostly used to achieve the capacity of communication networks. In this paper, motivated by the nanoscale communications where the energy cost for the channel symbols is asymmetric due to the widely employed on-off keying modulation, we design energy-minimizing network codes. We develop the best mapping between the input and output symbols at the network coding node that minimizes the average codeword energy using Latin squares, which we call the minimum energy network code (MENC). We define the class of networks composed of coding nodes with N incoming and 1 outgoing symbols as in-N networks. First, we derive the condition on the network code to minimize the average energy in in-two networks and propose two linear MENCs. Later, we investigate the MENCs for in-N networks using the Latin hypercubes and propose a low-energy network code (LENC) to reduce the average energy with network coding. We compare MENC with the classical XOR and random network codes for in-two networks. The performance comparison between LENC and random network codes for in-N networks shows that the proposed network codes provide significant energy gains.