Source Coding When the Side Information May Be Delayed

For memoryless sources, delayed side information at the decoder does not improve the rate-distortion function. However, this is not the case for more general sources with memory, as demonstrated by a number of works focusing on the special case of (delayed) feedforward. In this paper, a setting is studied in which the encoder is potentially uncertain about the delay with which measurements of the side information are acquired at the decoder. Assuming a hidden Markov model for the sources, at first, a single-letter characterization is given for the set-up where the side information delay is arbitrary and known at the encoder, and the reconstruction at the destination is required to be (near) lossless. Then, with delay equal to zero or one source symbol, a single-letter characterization is given of the rate-distortion region for the case where side information may be delayed or not, unbeknownst to the encoder. The characterization is further extended to allow for additional information to be sent when the side information is not delayed. Finally, examples for binary and Gaussian sources are provided.Comment: revised July 201

On the Effect of Correlated Measurements on the Performance of Distributed Estimation

We address the distributed estimation of an unknown scalar parameter in Wireless Sensor Networks (WSNs). Sensor nodes transmit their noisy observations over multiple access channel to a Fusion Center (FC) that reconstructs the source parameter. The received signal is corrupted by noise and channel fading, so that the FC objective is to minimize the Mean-Square Error (MSE) of the estimate. In this paper, we assume sensor node observations to be correlated with the source signal and correlated with each other as well. The correlation coefficient between two observations is exponentially decaying with the distance separation. The effect of the distance-based correlation on the estimation quality is demonstrated and compared with the case of unity correlated observations. Moreover, a closed-form expression for the outage probability is derived and its dependency on the correlation coefficients is investigated. Numerical simulations are provided to verify our analytic results.Comment: 5 page