7,631 research outputs found
A General Formula for the Mismatch Capacity
The fundamental limits of channels with mismatched decoding are addressed. A
general formula is established for the mismatch capacity of a general channel,
defined as a sequence of conditional distributions with a general decoding
metrics sequence. We deduce an identity between the Verd\'{u}-Han general
channel capacity formula, and the mismatch capacity formula applied to Maximum
Likelihood decoding metric. Further, several upper bounds on the capacity are
provided, and a simpler expression for a lower bound is derived for the case of
a non-negative decoding metric. The general formula is specialized to the case
of finite input and output alphabet channels with a type-dependent metric. The
closely related problem of threshold mismatched decoding is also studied, and a
general expression for the threshold mismatch capacity is obtained. As an
example of threshold mismatch capacity, we state a general expression for the
erasures-only capacity of the finite input and output alphabet channel. We
observe that for every channel there exists a (matched) threshold decoder which
is capacity achieving. Additionally, necessary and sufficient conditions are
stated for a channel to have a strong converse. Csisz\'{a}r and Narayan's
conjecture is proved for bounded metrics, providing a positive answer to the
open problem introduced in [1], i.e., that the "product-space" improvement of
the lower random coding bound, , is indeed the mismatch
capacity of the discrete memoryless channel . We conclude by presenting an
identity between the threshold capacity and in the DMC
case
Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities
This monograph presents a unified treatment of single- and multi-user
problems in Shannon's information theory where we depart from the requirement
that the error probability decays asymptotically in the blocklength. Instead,
the error probabilities for various problems are bounded above by a
non-vanishing constant and the spotlight is shone on achievable coding rates as
functions of the growing blocklengths. This represents the study of asymptotic
estimates with non-vanishing error probabilities.
In Part I, after reviewing the fundamentals of information theory, we discuss
Strassen's seminal result for binary hypothesis testing where the type-I error
probability is non-vanishing and the rate of decay of the type-II error
probability with growing number of independent observations is characterized.
In Part II, we use this basic hypothesis testing result to develop second- and
sometimes, even third-order asymptotic expansions for point-to-point
communication. Finally in Part III, we consider network information theory
problems for which the second-order asymptotics are known. These problems
include some classes of channels with random state, the multiple-encoder
distributed lossless source coding (Slepian-Wolf) problem and special cases of
the Gaussian interference and multiple-access channels. Finally, we discuss
avenues for further research.Comment: Further comments welcom
Collective Particle Flow through Random Media
A simple model for the nonlinear collective transport of interacting
particles in a random medium with strong disorder is introduced and analyzed. A
finite threshold for the driving force divides the behavior into two regimes
characterized by the presence or absence of a steady-state particle current.
Below this threshold, transient motion is found in response to an increase in
the force, while above threshold the flow approaches a steady state with motion
only on a network of channels which is sparse near threshold. Some of the
critical behavior near threshold is analyzed via mean field theory, and
analytic results on the statistics of the moving phase are derived. Many of the
results should apply, at least qualitatively, to the motion of magnetic bubble
arrays and to the driven motion of vortices in thin film superconductors when
the randomness is strong enough to destroy the tendencies to lattice order even
on short length scales. Various history dependent phenomena are also discussed.Comment: 63 preprint pages plus 6 figures. Submitted to Phys Rev
Bits About the Channel: Multi-round Protocols for Two-way Fading Channels
Most communication systems use some form of feedback, often related to
channel state information. In this paper, we study diversity multiplexing
tradeoff for both FDD and TDD systems, when both receiver and transmitter
knowledge about the channel is noisy and potentially mismatched. For FDD
systems, we first extend the achievable tradeoff region for 1.5 rounds of
message passing to get higher diversity compared to the best known scheme, in
the regime of higher multiplexing gains. We then break the mold of all current
channel state based protocols by using multiple rounds of conferencing to
extract more bits about the actual channel. This iterative refinement of the
channel increases the diversity order with every round of communication. The
protocols are on-demand in nature, using high powers for training and feedback
only when the channel is in poor states. The key result is that the diversity
multiplexing tradeoff with perfect training and K levels of perfect feedback
can be achieved, even when there are errors in training the receiver and errors
in the feedback link, with a multi-round protocol which has K rounds of
training and K-1 rounds of binary feedback. The above result can be viewed as a
generalization of Zheng and Tse, and Aggarwal and Sabharwal, where the result
was shown to hold for K=1 and K=2 respectively. For TDD systems, we also
develop new achievable strategies with multiple rounds of communication between
the transmitter and the receiver, which use the reciprocity of the forward and
the feedback channel. The multi-round TDD protocol achieves a
diversity-multiplexing tradeoff which uniformly dominates its FDD counterparts,
where no channel reciprocity is available.Comment: Submitted to IEEE Transactions on Information Theor
The Sender-Excited Secret Key Agreement Model: Capacity, Reliability and Secrecy Exponents
We consider the secret key generation problem when sources are randomly
excited by the sender and there is a noiseless public discussion channel. Our
setting is thus similar to recent works on channels with action-dependent
states where the channel state may be influenced by some of the parties
involved. We derive single-letter expressions for the secret key capacity
through a type of source emulation analysis. We also derive lower bounds on the
achievable reliability and secrecy exponents, i.e., the exponential rates of
decay of the probability of decoding error and of the information leakage.
These exponents allow us to determine a set of strongly-achievable secret key
rates. For degraded eavesdroppers the maximum strongly-achievable rate equals
the secret key capacity; our exponents can also be specialized to previously
known results.
In deriving our strong achievability results we introduce a coding scheme
that combines wiretap coding (to excite the channel) and key extraction (to
distill keys from residual randomness). The secret key capacity is naturally
seen to be a combination of both source- and channel-type randomness. Through
examples we illustrate a fundamental interplay between the portion of the
secret key rate due to each type of randomness. We also illustrate inherent
tradeoffs between the achievable reliability and secrecy exponents. Our new
scheme also naturally accommodates rate limits on the public discussion. We
show that under rate constraints we are able to achieve larger rates than those
that can be attained through a pure source emulation strategy.Comment: 18 pages, 8 figures; Submitted to the IEEE Transactions on
Information Theory; Revised in Oct 201
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