TY - JOUR
T1 - Asymmetric multilevel diversity coding and asymmetric Gaussian multiple descriptions
AU - Mohajer, Soheil
AU - Tian, Chao
AU - Diggavi, Suhas N.
PY - 2010/9
Y1 - 2010/9
N2 - We consider the asymmetric multilevel diversity (A-MLD) coding problem, where a set of 2K-1 information sources, ordered in a decreasing level of importance, is encoded into K messages (or descriptions). There are 2K-1 decoders, each of which has access to a nonempty subset of the encoded messages. Each decoder is required to reproduce the information sources up to a certain importance level depending on the combination of descriptions available to it. We obtain a single letter characterization of the achievable rate region for the 3-description problem. In contrast to symmetric multilevel diversity coding, source-separation coding is not sufficient in the asymmetric case, and ideas akin to network coding need to be used strategically. Based on the intuitions gained in treating the A-MLD problem, we derive inner and outer bounds for the rate region of the asymmetric Gaussian multiple description (MD) problem with three descriptions. Both the inner and outer bounds have a similar geometric structure to the rate region template of the A-MLD coding problem, and, moreover, we show that the gap between them is constant, which results in an approximate characterization of the asymmetric Gaussian three description rate region.
AB - We consider the asymmetric multilevel diversity (A-MLD) coding problem, where a set of 2K-1 information sources, ordered in a decreasing level of importance, is encoded into K messages (or descriptions). There are 2K-1 decoders, each of which has access to a nonempty subset of the encoded messages. Each decoder is required to reproduce the information sources up to a certain importance level depending on the combination of descriptions available to it. We obtain a single letter characterization of the achievable rate region for the 3-description problem. In contrast to symmetric multilevel diversity coding, source-separation coding is not sufficient in the asymmetric case, and ideas akin to network coding need to be used strategically. Based on the intuitions gained in treating the A-MLD problem, we derive inner and outer bounds for the rate region of the asymmetric Gaussian multiple description (MD) problem with three descriptions. Both the inner and outer bounds have a similar geometric structure to the rate region template of the A-MLD coding problem, and, moreover, we show that the gap between them is constant, which results in an approximate characterization of the asymmetric Gaussian three description rate region.
KW - Asymmetry
KW - multilevel diversity coding
KW - multiple descriptions
KW - rate-distortion
UR - http://www.scopus.com/inward/record.url?scp=77955721831&partnerID=8YFLogxK
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U2 - 10.1109/TIT.2010.2054535
DO - 10.1109/TIT.2010.2054535
M3 - Article
AN - SCOPUS:77955721831
SN - 0018-9448
VL - 56
SP - 4367
EP - 4387
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 9
M1 - 5550379
ER -