Distributed Source Coding in Dense Sensor Networks

Abstract

We study the problem of the reconstruction of a Gaussian field defined in [0, 1] using N sensors deployed at regular intervals. The goal is to quantify the total data rate required for the reconstruction of the field with a given mean square distortion. We consider a class of two-stage mechanisms which a) send information to allow the reconstruction of the sensor's samples within sufficient accuracy, and then b) use these reconstructions to estimate the entire field. To implement the first stage, the heavy correlation between the sensor samples suggests the use of distributed coding schemes to reduce the total rate. We demonstrate the existence of a distributed block coding scheme that achieves, for a given fidelity criterion for the reconstruction of the field, a total information rate that is bounded by a constant, independent of the number N of sensors. The constant in general depends on the autocorrelation function of the field and the desired distortion criterion for the sensor samples. We then describe a scheme which can be implemented using only scalar quantizers at the sensors, without any use of distributed source coding, and which also achieves a total information rate that is a constant, independent of the number of sensors. While this scheme operates at a rate that is greater than the rate achievable through distributed coding and entails greater delay in reconstruction, its simplicity makes it attractive for implementation in sensor networks.

Scaling Laws for Dense Gaussian Sensor Networks and the Order Optimality of Separation

“…We are interested in the performance in the information-theoretic sense and, hence, we allow the delay to be arbitrarily large. By the assumption of sum power constraint, we have (8) The collector node reconstructs the random process as (9) For fixed encoding functions of the nodes and the decoding function of the collector node , the achieved expected distortion is (10) and we are interested in the smallest achievable expected distortion over all encoding and decoding functions where is allowed to be arbitrarily large.…”

“…Kashyap et al [8] studied the source coding part of the problem investigated in this paper. The paper showed that for any distortion constraint that is independent of , the difference between the rate achievable by distributed source coding and the rate achievable by centralized source coding is bounded by a constant, independent of .…”

“…Though we study a joint source-channel coding problem, both our converse and achievability proofs are separation-based, and thus, we show a similar result: in the source coding part we show that the ratio between the rate achievable by distributed source coding and the rate achievable by centralized source coding is bounded by a constant, independent of . In contrast to [8], where the distortion constraint is independent of , we allow the distortion to go to zero as a function of . Moreover, [8] deals with stationary Gaussian random processes, while we allow for nonstationarity of the underlying random process.…”

“…In contrast to [8], where the distortion constraint is independent of , we allow the distortion to go to zero as a function of . Moreover, [8] deals with stationary Gaussian random processes, while we allow for nonstationarity of the underlying random process. It is not immediately evident whether the methods in [8] apply in the scenario considered in this paper.…”

“…Moreover, [8] deals with stationary Gaussian random processes, while we allow for nonstationarity of the underlying random process. It is not immediately evident whether the methods in [8] apply in the scenario considered in this paper.…”