Universal Lattice-Based Quantizers for Multiple Descriptions
DCC '00 Proceedings of the Conference on Data Compression
Multiple-description coding by dithered delta-sigma quantization
IEEE Transactions on Information Theory
N-channel asymmetric entropy-constrained multiple-description lattice vector quantization
IEEE Transactions on Information Theory
| Hi-index | 754.96 |
A pair of well-known inequalities, due to Shannon, upper/lower bound the rate-distortion function of a real source by the rate-distortion function of the Gaussian source with the same variance/entropy. We extend these bounds to multiple descriptions, a problem for which a general “single-letter” solution is not known. We show that the set DX(R1, R2) of achievable marginal (d1, d2) and central (d0) mean-squared errors in decoding X from two descriptions at rates R1 and R2 satisfies D*(σx2, R1, R2)⊆D X(R1, R2)⊆D*(Px, R1, R2) where σx2 and Px are the variance and the entropy-power of X, respectively, and D*(σ2, R1, R2) is the multiple description distortion region for a Gaussian source with variance σ2 found by Ozarow (1980). We further show that like in the single description case, a Gaussian random code achieves the outer bound in the limit as d1, d2→0, thus the outer bound is asymptotically tight at high resolution conditions