8,076 research outputs found
State Amplification
We consider the problem of transmitting data at rate R over a state dependent
channel p(y|x,s) with the state information available at the sender and at the
same time conveying the information about the channel state itself to the
receiver. The amount of state information that can be learned at the receiver
is captured by the mutual information I(S^n; Y^n) between the state sequence
S^n and the channel output Y^n. The optimal tradeoff is characterized between
the information transmission rate R and the state uncertainty reduction rate
\Delta, when the state information is either causally or noncausally available
at the sender. This result is closely related and in a sense dual to a recent
study by Merhav and Shamai, which solves the problem of masking the state
information from the receiver rather than conveying it.Comment: 9 pages, 4 figures, submitted to IEEE Trans. Inform. Theory, revise
Two-way quantum communication channels
We consider communication between two parties using a bipartite quantum
operation, which constitutes the most general quantum mechanical model of
two-party communication. We primarily focus on the simultaneous forward and
backward communication of classical messages. For the case in which the two
parties share unlimited prior entanglement, we give inner and outer bounds on
the achievable rate region that generalize classical results due to Shannon. In
particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a
one-shot expression in terms of the Holevo information for the
entanglement-assisted one-way capacity of a two-way quantum channel. As
applications, we rederive two known additivity results for one-way channel
capacities: the entanglement-assisted capacity of a general one-way channel,
and the unassisted capacity of an entanglement-breaking one-way channel.Comment: 21 pages, 3 figure
On Marton's inner bound for broadcast channels
Marton's inner bound is the best known achievable region for a general
discrete memoryless broadcast channel. To compute Marton's inner bound one has
to solve an optimization problem over a set of joint distributions on the input
and auxiliary random variables. The optimizers turn out to be structured in
many cases. Finding properties of optimizers not only results in efficient
evaluation of the region, but it may also help one to prove factorization of
Marton's inner bound (and thus its optimality). The first part of this paper
formulates this factorization approach explicitly and states some conjectures
and results along this line. The second part of this paper focuses primarily on
the structure of the optimizers. This section is inspired by a new binary
inequality that recently resulted in a very simple characterization of the
sum-rate of Marton's inner bound for binary input broadcast channels. This
prompted us to investigate whether this inequality can be extended to larger
cardinality input alphabets. We show that several of the results for the binary
input case do carry over for higher cardinality alphabets and we present a
collection of results that help restrict the search space of probability
distributions to evaluate the boundary of Marton's inner bound in the general
case. We also prove a new inequality for the binary skew-symmetric broadcast
channel that yields a very simple characterization of the entire Marton inner
bound for this channel.Comment: Submitted to ISIT 201
Critical Noise Levels for LDPC decoding
We determine the critical noise level for decoding low density parity check
error correcting codes based on the magnetization enumerator (\cM), rather
than on the weight enumerator (\cW) employed in the information theory
literature. The interpretation of our method is appealingly simple, and the
relation between the different decoding schemes such as typical pairs decoding,
MAP, and finite temperature decoding (MPM) becomes clear. In addition, our
analysis provides an explanation for the difference in performance between MN
and Gallager codes. Our results are more optimistic than those derived via the
methods of information theory and are in excellent agreement with recent
results from another statistical physics approach.Comment: 9 pages, 5 figure
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