37 research outputs found
How to Quantize Outputs of a Binary Symmetric Channel to Bits?
Suppose that is obtained by observing a uniform Bernoulli random vector
through a binary symmetric channel with crossover probability .
The "most informative Boolean function" conjecture postulates that the maximal
mutual information between and any Boolean function is
attained by a dictator function. In this paper, we consider the "complementary"
case in which the Boolean function is replaced by
, namely, an bit
quantizer, and show that
for any such . Thus, in this case, the optimal function is of the form
.Comment: 5 pages, accepted ISIT 201
Analysis of Mismatched Estimation Errors Using Gradients of Partition Functions
We consider the problem of signal estimation (denoising) from a
statistical-mechanical perspective, in continuation to a recent work on the
analysis of mean-square error (MSE) estimation using a direct relationship
between optimum estimation and certain partition functions. The paper consists
of essentially two parts. In the first part, using the aforementioned
relationship, we derive single-letter expressions of the mismatched MSE of a
codeword (from a randomly selected code), corrupted by a Gaussian vector
channel. In the second part, we provide several examples to demonstrate phase
transitions in the behavior of the MSE. These examples enable us to understand
more deeply and to gather intuition regarding the roles of the real and the
mismatched probability measures in creating these phase transitions.Comment: 58 pages;Submitted to IEEE Trans. on Information Theor
Channels with Cooperation Links that May Be Absent
It is well known that cooperation between users in a communication network
can lead to significant performance gains. A common assumption in past works is
that all the users are aware of the resources available for cooperation, and
know exactly to what extent these resources can be used. Unfortunately, in many
modern communication networks the availability of cooperation links cannot be
guaranteed a priori, due to the dynamic nature of the network. In this work a
family of models is suggested where the cooperation links may or may not be
present. Coding schemes are devised that exploit the cooperation links if they
are present, and can still operate (although at reduced rates) if cooperation
is not possible.Comment: Accepted for publication in the IEEE transaction on Information
Theory, June 201
Random Coding Error Exponents for the Two-User Interference Channel
This paper is about deriving lower bounds on the error exponents for the
two-user interference channel under the random coding regime for several
ensembles. Specifically, we first analyze the standard random coding ensemble,
where the codebooks are comprised of independently and identically distributed
(i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is
in contrast to other, suboptimal decoding rules that have been used in the
literature (e.g., joint typicality decoding, treating interference as noise,
etc.). The fact that the interfering signal is a codeword, rather than an
i.i.d. noise process, complicates the application of conventional techniques of
performance analysis of the optimum decoder. Also, unfortunately, these
conventional techniques result in loose bounds. Using analytical tools rooted
in statistical physics, as well as advanced union bounds, we derive
single-letter formulas for the random coding error exponents. We compare our
results with the best known lower bound on the error exponent, and show that
our exponents can be strictly better. Then, in the second part of this paper,
we consider more complicated coding ensembles, and find a lower bound on the
error exponent associated with the celebrated Han-Kobayashi (HK) random coding
ensemble, which is based on superposition coding.Comment: accepted IEEE Transactions on Information Theor
Design of Discrete Constellations for Peak-Power-Limited complex Gaussian Channels
Proceeding of: IEEE International Symposium on Information Theory (ISIT 2018)The capacity-achieving input distribution of the complex Gaussian channel with both average- and peak-power constraint is known to have a discrete amplitude and a continuous, uniformly-distributed, phase. Practical considerations, however, render the continuous phase inapplicable. This work studies the backoff from capacity induced by discretizing the phase of the input signal. A sufficient condition on the total number of quantization points that guarantees an arbitrarily small backoff is derived, and constellations that attain this guaranteed performance are proposed.The work of W. Huleihel was supported by the MIT - Technion Postdoctoral Fellowship. The work of Z. Goldfeld was supported by the Rothchild postdoctoral fellowship. The work of T. Koch has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the Spanish Ministerio de EconomÃıa y Competitividad under Grants TEC2013-41718-R, RYC-2014-16332, and TEC2016-78434-C3-3-R (AEI/FEDER, EU), and from the Comunidad de Madrid under Grant S2103/ICE-2845. The work of M. Mokshay was supported by NSF grant #1409504