1,296 research outputs found
On the BICM Capacity
Optimal binary labelings, input distributions, and input alphabets are
analyzed for the so-called bit-interleaved coded modulation (BICM) capacity,
paying special attention to the low signal-to-noise ratio (SNR) regime. For
8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded
binary code results in a higher capacity than the binary reflected gray code
(BRGC) and the natural binary code (NBC). The 1 dB gap between the additive
white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be
almost completely removed if the input symbol distribution is properly
selected. First-order asymptotics of the BICM capacity for arbitrary input
alphabets and distributions, dimensions, mean, variance, and binary labeling
are developed. These asymptotics are used to define first-order optimal (FOO)
constellations for BICM, i.e. constellations that make BICM achieve the Shannon
limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable
transmission at asymptotically low rates in BICM can be as high as infinity,
that for uniform input distributions and 8-PAM there are only 72 classes of
binary labelings with a different first-order asymptotic behavior, and that
this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general
answer to the question of FOO constellations for BICM is also given: using the
Hadamard transform, it is found that for uniform input distributions, a
constellation for BICM is FOO if and only if it is a linear projection of a
hypercube. A constellation based on PAM or quadrature amplitude modulation
input alphabets is FOO if and only if they are labeled by the NBC; if the
constellation is based on PSK input alphabets instead, it can never be FOO if
the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor
Finite-Block-Length Analysis in Classical and Quantum Information Theory
Coding technology is used in several information processing tasks. In
particular, when noise during transmission disturbs communications, coding
technology is employed to protect the information. However, there are two types
of coding technology: coding in classical information theory and coding in
quantum information theory. Although the physical media used to transmit
information ultimately obey quantum mechanics, we need to choose the type of
coding depending on the kind of information device, classical or quantum, that
is being used. In both branches of information theory, there are many elegant
theoretical results under the ideal assumption that an infinitely large system
is available. In a realistic situation, we need to account for finite size
effects. The present paper reviews finite size effects in classical and quantum
information theory with respect to various topics, including applied aspects
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
Fundamental Finite Key Limits for One-Way Information Reconciliation in Quantum Key Distribution
The security of quantum key distribution protocols is guaranteed by the laws
of quantum mechanics. However, a precise analysis of the security properties
requires tools from both classical cryptography and information theory. Here,
we employ recent results in non-asymptotic classical information theory to show
that one-way information reconciliation imposes fundamental limitations on the
amount of secret key that can be extracted in the finite key regime. In
particular, we find that an often used approximation for the information
leakage during information reconciliation is not generally valid. We propose an
improved approximation that takes into account finite key effects and
numerically test it against codes for two probability distributions, that we
call binary-binary and binary-Gaussian, that typically appear in quantum key
distribution protocols
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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