277 research outputs found
A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels
This paper shows that the logarithm of the epsilon-error capacity (average
error probability) for n uses of a discrete memoryless channel is upper bounded
by the normal approximation plus a third-order term that does not exceed 1/2
log n + O(1) if the epsilon-dispersion of the channel is positive. This matches
a lower bound by Y. Polyanskiy (2010) for discrete memoryless channels with
positive reverse dispersion. If the epsilon-dispersion vanishes, the logarithm
of the epsilon-error capacity is upper bounded by the n times the capacity plus
a constant term except for a small class of DMCs and epsilon >= 1/2.Comment: published versio
The third-order term in the normal approximation for singular channels
For a singular and symmetric discrete memoryless channel with positive
dispersion, the third-order term in the normal approximation is shown to be
upper bounded by a constant. This finding completes the characterization of the
third-order term for symmetric discrete memoryless channels. The proof method
is extended to asymmetric and singular channels with constant composition
codes, and its connection to existing results, as well as its limitation in the
error exponents regime, are discussed.Comment: Submitted to IEEE Trans. Inform. Theor
Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
We study non-asymptotic fundamental limits for transmitting classical
information over memoryless quantum channels, i.e. we investigate the amount of
classical information that can be transmitted when a quantum channel is used a
finite number of times and a fixed, non-vanishing average error is permissible.
We consider the classical capacity of quantum channels that are image-additive,
including all classical to quantum channels, as well as the product state
capacity of arbitrary quantum channels. In both cases we show that the
non-asymptotic fundamental limit admits a second-order approximation that
illustrates the speed at which the rate of optimal codes converges to the
Holevo capacity as the blocklength tends to infinity. The behavior is governed
by a new channel parameter, called channel dispersion, for which we provide a
geometrical interpretation.Comment: v2: main results significantly generalized and improved; v3: extended
to image-additive channels, change of title, journal versio
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
Second-Order Coding Rates for Channels with State
We study the performance limits of state-dependent discrete memoryless
channels with a discrete state available at both the encoder and the decoder.
We establish the epsilon-capacity as well as necessary and sufficient
conditions for the strong converse property for such channels when the sequence
of channel states is not necessarily stationary, memoryless or ergodic. We then
seek a finer characterization of these capacities in terms of second-order
coding rates. The general results are supplemented by several examples
including i.i.d. and Markov states and mixed channels
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