1,566 research outputs found
The AWGN Red Alert Problem
Consider the following unequal error protection scenario. One special
message, dubbed the "red alert" message, is required to have an extremely small
probability of missed detection. The remainder of the messages must keep their
average probability of error and probability of false alarm below a certain
threshold. The goal then is to design a codebook that maximizes the error
exponent of the red alert message while ensuring that the average probability
of error and probability of false alarm go to zero as the blocklength goes to
infinity. This red alert exponent has previously been characterized for
discrete memoryless channels. This paper completely characterizes the optimal
red alert exponent for additive white Gaussian noise channels with block power
constraints.Comment: 13 pages, 10 figures, To appear in IEEE Transactions on Information
Theor
Optimal Detector Randomization in Cognitive Radio Systems in the Presence of Imperfect Sensing Decisions
Cataloged from PDF version of article.In this study, optimal detector randomization is developed for secondary users in a cognitive radio system in the presence of imperfect spectrum sensing decisions. It is shown that the minimum average probability of error can be achieved by employing no more than four maximum a-posteriori probability (MAP) detectors at the secondary receiver. Optimal MAP detectors and generic expressions for their average probability of error are derived in the presence of possible sensing errors. Also, sufficient conditions are presented related to improvements due to optimal detector randomization. © 2014 IEEE
Finite Blocklength Rates over a Fading Channel with CSIT and CSIR
In this work, we obtain lower and upper bounds on the maximal transmission
rate at a given codeword length , average probability of error
and power constraint , over a finite valued, block fading additive
white Gaussian noise (AWGN) channel with channel state information (CSI) at the
transmitter and the receiver. These bounds characterize deviation of the finite
blocklength coding rates from the channel capacity which is in turn achieved by
the water filling power allocation across time. The bounds obtained also
characterize the rate enhancement possible due to the CSI at the transmitter in
the finite blocklength regime. The results are further elucidated via numerical
examples.Comment: 10 pages, 2 figures, results for finite valued fading states, typos
corrected, proofs elaborated, lower bound under short term power constraint
improve
Reliable Quantum Computers
The new field of quantum error correction has developed spectacularly since
its origin less than two years ago. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment. Recovery from errors can work effectively even if occasional
mistakes occur during the recovery procedure. Furthermore, encoded quantum
information can be processed without serious propagation of errors. Hence, an
arbitrarily long quantum computation can be performed reliably, provided that
the average probability of error per quantum gate is less than a certain
critical value, the accuracy threshold. A quantum computer storing about 10^6
qubits, with a probability of error per quantum gate of order 10^{-6}, would be
a formidable factoring engine. Even a smaller, less accurate quantum computer
would be able to perform many useful tasks. (This paper is based on a talk
presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18
December 1996.)Comment: 24 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor
correction
Fault-tolerant quantum computation
The discovery of quantum error correction has greatly improved the long-term
prospects for quantum computing technology. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment, or due to imperfect implementations of quantum logical operations.
Recovery from errors can work effectively even if occasional mistakes occur
during the recovery procedure. Furthermore, encoded quantum information can be
processed without serious propagation of errors. In principle, an arbitrarily
long quantum computation can be performed reliably, provided that the average
probability of error per gate is less than a certain critical value, the
accuracy threshold. It may be possible to incorporate intrinsic fault tolerance
into the design of quantum computing hardware, perhaps by invoking topological
Aharonov-Bohm interactions to process quantum information.Comment: 58 pages with 7 PostScript figures, LaTeX, uses sprocl.sty and psfig,
to appear in "Introduction to Quantum Computation," edited by H.-K. Lo, S.
Popescu, and T. P. Spille
Bounds on inference
Lower bounds for the average probability of error of estimating a hidden
variable X given an observation of a correlated random variable Y, and Fano's
inequality in particular, play a central role in information theory. In this
paper, we present a lower bound for the average estimation error based on the
marginal distribution of X and the principal inertias of the joint distribution
matrix of X and Y. Furthermore, we discuss an information measure based on the
sum of the largest principal inertias, called k-correlation, which generalizes
maximal correlation. We show that k-correlation satisfies the Data Processing
Inequality and is convex in the conditional distribution of Y given X. Finally,
we investigate how to answer a fundamental question in inference and privacy:
given an observation Y, can we estimate a function f(X) of the hidden random
variable X with an average error below a certain threshold? We provide a
general method for answering this question using an approach based on
rate-distortion theory.Comment: Allerton 2013 with extended proof, 10 page
Memoryless Relay Strategies for Two-Way Relay Channels: Performance Analysis and Optimization
We consider relaying strategies for two-way relay channels, where two terminals transmits simultaneously to each other with the help of relays. A memoryless system is considered, where the signal transmitted by a relay depends only on its last received signal. For binary antipodal signaling, we analyze and optimize the performance of existing amplify and forward (AF) and absolute (abs) decode and forward (ADF) for two- way AWGN relay channels. A new abs-based AF (AAF) scheme is proposed, which has better performance than AF. In low SNR, AAF performs even better than ADF. Furthermore, a novel estimate and forward (EF) strategy is proposed which performs better than ADF. More importantly, we optimize the relay strategy within the class of abs-based strategies via functional analysis, which minimizes the average probability of error over all possible relay functions. The optimized function is shown to be a Lambert's W function parameterized on the noise power and the transmission energy. The optimized function behaves like AAF in low SNR and like ADF in high SNR, resp., where EF behaves like the optimized function over the whole SNR range
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