On the Role of Feedforward in Gaussian Sources: Point-to-Point Source Coding and Multiple Description Source Coding

Source coding with noiseless feedforward deals with efficient quantization of information sources into indexes, where to reconstruct a source sample, the decoder in addition to this index, has access to all the previous noiseless source samples. This problem may find applications in sensor networks, economics, and control theory. In the first part of this paper, we consider a deterministic block coding scheme for independent and identically distributed (i.i.d.) Gaussian sources. We show that this scheme is asymptotically optimal in terms of its rate-distortion function and the error exponent. In the second part of this paper we consider two-channel multiple description source coding with noiseless feedforward. We consider i.i.d. Gaussian sources and obtain the optimal rate-distortion region. The key result is that there is no penalty to be paid for constraining the descriptions to be mutually refineable. That is when one of the channels is active, the decoder which operates on one of the descriptions achieves the optimal rate-distortion function, and when both channels are active, the joint decoder still attains the optimal rate-distortion function. This implies that for memoryless sources with additive distortion measures, in the case of multiple description source coding, noiseless feedforward provides significant improvements in performance. We then evaluate the optimal multiple description source coding error exponents for the symmetric case