3 research outputs found
Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information
We consider the -user successive refinement problem with causal decoder
side information and derive an exponential strong converse theorem. The
rate-distortion region for the problem can be derived as a straightforward
extension of the two-user case by Maor and Merhav (2008). We show that for any
rate-distortion tuple outside the rate-distortion region of the -user
successive refinement problem with causal decoder side information, the joint
excess-distortion probability approaches one exponentially fast. Our proof
follows by judiciously adapting the recently proposed strong converse technique
by Oohama using the information spectrum method, the variational form of the
rate-distortion region and H\"older's inequality. The lossy source coding
problem with causal decoder side information considered by El Gamal and
Weissman is a special case () of the current problem. Therefore, the
exponential strong converse theorem for the El Gamal and Weissman problem
follows as a corollary of our result
Source Coding When the Side Information May Be Delayed
For memoryless sources, delayed side information at the decoder does not
improve the rate-distortion function. However, this is not the case for more
general sources with memory, as demonstrated by a number of works focusing on
the special case of (delayed) feedforward. In this paper, a setting is studied
in which the encoder is potentially uncertain about the delay with which
measurements of the side information are acquired at the decoder. Assuming a
hidden Markov model for the sources, at first, a single-letter characterization
is given for the set-up where the side information delay is arbitrary and known
at the encoder, and the reconstruction at the destination is required to be
(near) lossless. Then, with delay equal to zero or one source symbol, a
single-letter characterization is given of the rate-distortion region for the
case where side information may be delayed or not, unbeknownst to the encoder.
The characterization is further extended to allow for additional information to
be sent when the side information is not delayed. Finally, examples for binary
and Gaussian sources are provided.Comment: revised July 201
Source Coding Problems with Conditionally Less Noisy Side Information
A computable expression for the rate-distortion (RD) function proposed by
Heegard and Berger has eluded information theory for nearly three decades.
Heegard and Berger's single-letter achievability bound is well known to be
optimal for \emph{physically degraded} side information; however, it is not
known whether the bound is optimal for arbitrarily correlated side information
(general discrete memoryless sources). In this paper, we consider a new setup
in which the side information at one receiver is \emph{conditionally less
noisy} than the side information at the other. The new setup includes degraded
side information as a special case, and it is motivated by the literature on
degraded and less noisy broadcast channels. Our key contribution is a converse
proving the optimality of Heegard and Berger's achievability bound in a new
setting. The converse rests upon a certain \emph{single-letterization} lemma,
which we prove using an information theoretic telescoping identity {recently
presented by Kramer}. We also generalise the above ideas to two different
successive-refinement problems