TY - JOUR
T1 - Gaussian codes and shannon bounds for multiple descriptions
AU - Zamir, Ram
PY - 1999
Y1 - 1999
N2 - A pair of well-known inequalities due to Shannon upper/lowerbound 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-letter̊ 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) ⊆ DX(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. 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.
AB - A pair of well-known inequalities due to Shannon upper/lowerbound 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-letter̊ 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) ⊆ DX(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. 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.
KW - Gaussian codes
KW - High resolution
KW - Multiple descriptions
KW - Shannon lower bound
UR - http://www.scopus.com/inward/record.url?scp=0032606371&partnerID=8YFLogxK
U2 - 10.1109/18.796418
DO - 10.1109/18.796418
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AN - SCOPUS:0032606371
SN - 0018-9448
VL - 45
SP - 2629
EP - 2636
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 7
ER -