Energy Minimization With Network Coding via Latin Hypercubes

Abstract

Network coding is mostly used to achieve the capacity of communication networks. In this study, motivated by the nanoscale communications where the energy cost for the channel symbols are asymmetric due to the widely employed OOK modulation, we design energy minimizing network codes. We develop the best mapping between the input and the 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 InN 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 minimum energy network codes for InN 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 InN networks shows that the proposed network codes provide significant energy gains. Index Terms-energy efficient network codes, green communications, minimum energy coding, network coding, latin squares. I. INTRODUCTION Network coding is the method of combining the information flows at the relay node, which is essential to achieve the network capacity in certain networks, as routing only is not sufficient in general [1]. From the day it was first proposed, network coding has drawn great interest from the community. In addition to purely information theoretic analyses, researchers have incorporated network coding into various subjects, from cognitive radio to ad-hoc networks [4], [9] to vehicular networks [2], [3]. Even though the main research on network coding focuses on achieving the network capacity, or its gains in terms of the achievable rate [1]-[8], there are several papers discussing the energy efficiency aspects of network coding [9]-[14]. However, in most of these studies, network coding is not used directly as a tool to minimize the