A Fully Polynomial Approximation Algorithm for Collaborative Relaying in Sensor Networks Under Finite Rate Constraints

Abstract

We take an algorithmic approach to a well-known communication channel problem and develop several algorithms for solving it. Specifically, we develop power control algorithms for sensor networks with collaborative relaying under bandwidth constraints, via quantization of finite rate (bandwidth limited) feedback channels. We first consider the power allocation problem under collaborative relaying where the tradeoff between minimizing ones own energy expenditure and the energy for relaying is considered under the constraints of packet outage probability and bandwidth constrained (finite rate) feedback. Then we develop bandwidth constrained quantization algorithms (due to the finite rate feedback) that seek the optimal way of quantizing channel quality and power values in order to minimize the total average transmission power and satisfy the given probability of outage. We develop two kinds of quantization protocols and associated quantization algorithms. For separate source-relay quantization, we reduce the problem to the well-known k-median problem [1] on line graphs and show a a simple $O((K_J)^2N)$ polynomial time algorithm, where log₂ K _J is the quantization bandwidth and N is the size of the discretized parameter space. For joint quantization, we first develop a simple 2-factor approximation of complexity O(K _J N + N logN). Then, for ε> 0, we develop a fully polynomial approximation scheme (FPAS) that approximates the optimal quantization cost to within an 1 + ε-factor. The running time of the FPAS is polynomial in 1/ε, size of the input N and also ln F, where F is the maximum available transmit power.

This work was supported by NSF grants IIS-0329738, ITR-0312632 and by AFRL under contract #F33615-02-D-1283 (sub #05-2D1005.001). The opinions expressed herein are those of the individual authors and independent of the sponsoring agencies.