34 research outputs found
The Likelihood Encoder for Lossy Compression
A likelihood encoder is studied in the context of lossy source compression.
The analysis of the likelihood encoder is based on the soft-covering lemma. It
is demonstrated that the use of a likelihood encoder together with the
soft-covering lemma yields simple achievability proofs for classical source
coding problems. The cases of the point-to-point rate-distortion function, the
rate-distortion function with side information at the decoder (i.e. the
Wyner-Ziv problem), and the multi-terminal source coding inner bound (i.e. the
Berger-Tung problem) are examined in this paper. Furthermore, a non-asymptotic
analysis is used for the point-to-point case to examine the upper bound on the
excess distortion provided by this method. The likelihood encoder is also
related to a recent alternative technique using properties of random binning
An upper bound on relaying over capacity based on channel simulation
The upper bound on the capacity of a 3-node discrete memoryless relay channel
is considered, where a source X wants to send information to destination Y with
the help of a relay Z. Y and Z are independent given X, and the link from Z to
Y is lossless with rate . A new inequality is introduced to upper-bound
the capacity when the encoding rate is beyond the capacities of both individual
links XY and XZ. It is based on generalization of the blowing-up lemma, linking
conditional entropy to decoding error, and channel simulation, to the case with
side information. The achieved upper-bound is strictly better than the
well-known cut-set bound in several cases when the latter is , with
being the channel capacity between X and Y. One particular case is
when the channel is statistically degraded, i.e., either Y is a statistically
degraded version of Z with respect to X, or Z is a statistically degraded
version of Y with respect to X. Moreover in this case, the bound is shown to be
explicitly computable. The binary erasure channel is analyzed in detail and
evaluated numerically.Comment: Submitted to IEEE Transactions on Information Theory, 21 pages, 6
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Secure Cascade Channel Synthesis
We consider the problem of generating correlated random variables in a
distributed fashion, where communication is constrained to a cascade network.
The first node in the cascade observes an i.i.d. sequence locally before
initiating communication along the cascade. All nodes share bits of common
randomness that are independent of . We consider secure synthesis - random
variables produced by the system appear to be appropriately correlated and
i.i.d. even to an eavesdropper who is cognizant of the communication
transmissions. We characterize the optimal tradeoff between the amount of
common randomness used and the required rates of communication. We find that
not only does common randomness help, its usage exceeds the communication rate
requirements. The most efficient scheme is based on a superposition codebook,
with the first node selecting messages for all downstream nodes. We also
provide a fleeting view of related problems, demonstrating how the optimal rate
region may shrink or expand.Comment: Submitted to IEEE Transactions on Information Theor