A Scaling Theory for Distributed Sparse Matrix Coding in the CEO Problem

We consider the problem of distributed sensing in a noisy environment; the CEO problem. Here individual sensor readings are encoded and transmitted independently by multiple sensors with a limited combined data rate. We present a scaling analysis of a semi-practical system using the sparse matrix codes, and show that the analysis is consistent with a general argument based on an existence of the rate distortion function. This approach well describes the tradeoff between reducing errors due to environmental noise and increasing errors due to lossy coding as the number of sensors increases, showing threshold behavior for optimal number of sensors