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n-channel symmetric multiple descriptions - part I: (n, k) source-channel erasure codes

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3 Author(s)
Pradhan, S.S. ; Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA ; Rohit Puri ; Ramchandran, K.

In this two-part paper, we present a new achievable rate region for the general n-channel symmetric multiple descriptions problem. In part I, inspired by the concept of maximum-distance separable (MDS) erasure channel codes, we consider a special case of this rate region, where the source is encoded into n descriptions each with rate R. These descriptions are transmitted over n bandwidth constrained and errorless channels. During transmission, a subset of these channels can break down, thus erasing the corresponding descriptions. The decoder is interested in recovering the source with the reception of at least k descriptions. Thus, the encoder is allowed to sample only one realization of this breakdown process during the entire transmission. For Gaussian sources, we have the following interesting result: when any k descriptions arrive, the achievable distortion exactly matches the optimal distortion-rate performance corresponding to a source rate of kR bits; with the reception of any m > k descriptions, the source reconstruction quality is strictly better, the improvement being nearly linear in the number of descriptions received.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 1 )