580 research outputs found
Asymmetric Evaluations of Erasure and Undetected Error Probabilities
The problem of channel coding with the erasure option is revisited for
discrete memoryless channels. The interplay between the code rate, the
undetected and total error probabilities is characterized. Using the
information spectrum method, a sequence of codes of increasing blocklengths
is designed to illustrate this tradeoff. Furthermore, for additive discrete
memoryless channels with uniform input distribution, we establish that our
analysis is tight with respect to the ensemble average. This is done by
analysing the ensemble performance in terms of a tradeoff between the code
rate, the undetected and the total errors. This tradeoff is parametrized by the
threshold in a generalized likelihood ratio test. Two asymptotic regimes are
studied. First, the code rate tends to the capacity of the channel at a rate
slower than corresponding to the moderate deviations regime. In this
case, both error probabilities decay subexponentially and asymmetrically. The
precise decay rates are characterized. Second, the code rate tends to capacity
at a rate of . In this case, the total error probability is
asymptotically a positive constant while the undetected error probability
decays as for some . The proof techniques involve
applications of a modified (or "shifted") version of the G\"artner-Ellis
theorem and the type class enumerator method to characterize the asymptotic
behavior of a sequence of cumulant generating functions.Comment: 28 pages, no figures in IEEE Transactions on Information Theory, 201
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
Tiny Codes for Guaranteeable Delay
Future 5G systems will need to support ultra-reliable low-latency
communications scenarios. From a latency-reliability viewpoint, it is
inefficient to rely on average utility-based system design. Therefore, we
introduce the notion of guaranteeable delay which is the average delay plus
three standard deviations of the mean. We investigate the trade-off between
guaranteeable delay and throughput for point-to-point wireless erasure links
with unreliable and delayed feedback, by bringing together signal flow
techniques to the area of coding. We use tiny codes, i.e. sliding window by
coding with just 2 packets, and design three variations of selective-repeat ARQ
protocols, by building on the baseline scheme, i.e. uncoded ARQ, developed by
Ausavapattanakun and Nosratinia: (i) Hybrid ARQ with soft combining at the
receiver; (ii) cumulative feedback-based ARQ without rate adaptation; and (iii)
Coded ARQ with rate adaptation based on the cumulative feedback. Contrasting
the performance of these protocols with uncoded ARQ, we demonstrate that HARQ
performs only slightly better, cumulative feedback-based ARQ does not provide
significant throughput while it has better average delay, and Coded ARQ can
provide gains up to about 40% in terms of throughput. Coded ARQ also provides
delay guarantees, and is robust to various challenges such as imperfect and
delayed feedback, burst erasures, and round-trip time fluctuations. This
feature may be preferable for meeting the strict end-to-end latency and
reliability requirements of future use cases of ultra-reliable low-latency
communications in 5G, such as mission-critical communications and industrial
control for critical control messaging.Comment: to appear in IEEE JSAC Special Issue on URLLC in Wireless Network
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