Searcharxiv⌕ Search

arXiv subjects

Erixhen Sula

Publications and source records attributed to Erixhen Sula.

12 recordsLinked to original sources
arXiv2024

Shannon Bounds for Quadratic Rate-Distortion Problems

The Shannon lower bound has been the subject of several important contributions by Berger. This paper surveys Shannon bounds on rate-distortion problems under mean-squared error distortion with a particular emphasis on Berger's techniques. Moreover, as a new result, the Gray-Wyner network is added to the canon of settings for which such bounds are known. In the Shannon bounding technique, elegant lower bounds are expressed in terms of the source entropy power. Moreover, there is often a complementary upper bound that involves the source variance in such a way that the bounds coincide in the special case of Gaussian statistics. Such pairs of bounds are sometimes referred to as Shannon bounds. The present paper puts Berger's work on many aspects of this problem in the context of more recent developments, encompassing indirect and remote source coding such as the CEO problem, originally proposed by Berger, as well as the Gray-Wyner network as a new contribution.

cs.IT↗
arXiv2023

On Semi-Supervised Estimation of Distributions

We study the problem of estimating the joint probability mass function (pmf) over two random variables. In particular, the estimation is based on the observation of $m$ samples containing both variables and $n$ samples missing one fixed variable. We adopt the minimax framework with $l^p_p$ loss functions, and we show that the composition of uni-variate minimax estimators achieves minimax risk with the optimal first-order constant for $p \ge 2$, in the regime $m = o(n)$.

math.ST↗
arXiv2022

On the Semi-supervised Expectation Maximization

The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples. Existing work in the semi-supervised case has focused mainly on performance rather than convergence guarantee, however we focus on the contribution of the labeled samples to the convergence rate. The analysis clearly demonstrates how the labeled samples improve the convergence rate for the exponential family mixture model. In this case, we assume that the population EM (EM with unlimited data) is initialized within the neighborhood of global convergence for the population EM that consists solely of samples that have not been labeled. The analysis for the labeled samples provides a comprehensive description of the convergence rate for the Gaussian mixture model. In addition, we extend the findings for labeled samples and offer an alternative proof for the population EM's convergence rate with unlabeled samples for the symmetric mixture of two Gaussians.

cs.LG↗
arXiv2022

Shannon Bounds on Lossy Gray-Wyner Networks

The Gray-Wyner network subject to a fidelity criterion is studied. Upper and lower bounds for the trade-offs between the private sum-rate and the common rate are obtained for arbitrary sources subject to mean-squared error distortion. The bounds meet exactly, leading to the computation of the rate region, when the source is jointly Gaussian. They meet partially when the sources are modeled via an additive Gaussian "channel". The bounds are inspired from the Shannon bounds on the rate-distortion problem.

cs.IT↗
arXiv2021

Lower bound on Wyner's Common Information

An important notion of common information between two random variables is due to Wyner. In this paper, we derive a lower bound on Wyner's common information for continuous random variables. The new bound improves on the only other general lower bound on Wyner's common information, which is the mutual information. We also show that the new lower bound is tight for the so-called "Gaussian channels" case, namely, when the joint distribution of the random variables can be written as the sum of a single underlying random variable and Gaussian noises. We motivate this work from the recent variations of Wyner's common information and applications to network data compression problems such as the Gray-Wyner network.

cs.IT↗
arXiv2020

The Gaussian lossy Gray-Wyner network

We consider the problem of source coding subject to a fidelity criterion for the Gray-Wyner network that connects a single source with two receivers via a common channel and two private channels. The pareto-optimal trade-offs between the sum-rate of the private channels and the rate of the common channel is completely characterized for jointly Gaussian sources subject to the mean-squared error criterion, leveraging convex duality and an argument involving the factorization of convex envelopes. Specifically, it is attained by selecting the auxiliary random variable to be jointly Gaussian with the sources.

cs.IT↗
arXiv2020

On Wyner's Common Information in the Gaussian Case

Wyner's Common Information and a natural relaxation are studied in the special case of Gaussian random variables. The relaxation replaces conditional independence by a bound on the conditional mutual information. The main contribution is the proof that Gaussian auxiliaries are optimal, leading to a closed-form formula. As a corollary, the proof technique also establishes the optimality of Gaussian auxiliaries for the Gaussian Gray-Wyner network, a long-standing open problem.

cs.IT↗
arXiv2020

Common Information Components Analysis

We give an information-theoretic interpretation of Canonical Correlation Analysis (CCA) via (relaxed) Wyner's common information. CCA permits to extract from two high-dimensional data sets low-dimensional descriptions (features) that capture the commonalities between the data sets, using a framework of correlations and linear transforms. Our interpretation first extracts the common information up to a pre-selected resolution level, and then projects this back onto each of the data sets. In the case of Gaussian statistics, this procedure precisely reduces to CCA, where the resolution level specifies the number of CCA components that are extracted. This also suggests a novel algorithm, Common Information Components Analysis (CICA), with several desirable features, including a natural extension to beyond just two data sets.

cs.IT↗
arXiv2020

Supply-Power-Constrained Cable Capacity Maximization Using Multi-Layer Neural Networks

We experimentally solve the problem of maximizing capacity under a total supply power constraint in a massively parallel submarine cable context, i.e., for a spatially uncoupled system in which fiber Kerr nonlinearity is not a dominant limitation. By using multi-layer neural networks trained with extensive measurement data acquired from a 12-span 744-km optical fiber link as an accurate digital twin of the true optical system, we experimentally maximize fiber capacity with respect to the transmit signal's spectral power distribution based on a gradient-descent algorithm. By observing convergence to approximately the same maximum capacity and power distribution for almost arbitrary initial conditions, we conjecture that the capacity surface is a concave function of the transmit signal power distribution. We then demonstrate that eliminating gain flattening filters (GFFs) from the optical amplifiers results in substantial capacity gains per Watt of electrical supply power compared to a conventional system that contains GFFs.

eess.SP↗
arXiv2018

Sum-Rate Capacity for Symmetric Gaussian Multiple Access Channels with Feedback

The feedback sum-rate capacity is established for the symmetric $J$-user Gaussian multiple-access channel (GMAC). The main contribution is a converse bound that combines the dependence-balance argument of Hekstra and Willems (1989) with a variant of the factorization of a convex envelope of Geng and Nair (2014). The converse bound matches the achievable sum-rate of the Fourier-Modulated Estimate Correction strategy of Kramer (2002).

cs.IT↗
arXiv2017

Compute--Forward Multiple Access (CFMA): Practical Code Design

We present a practical strategy that aims to attain rate points on the dominant face of the multiple access channel capacity using a standard low complexity decoder. This technique is built upon recent theoretical developments of Zhu and Gastpar on compute-forward multiple access (CFMA) which achieves the capacity of the multiple access channel using a sequential decoder. We illustrate this strategy with off-the-shelf LDPC codes. In the first stage of decoding, the receiver first recovers a linear combination of the transmitted codewords using the sum-product algorithm (SPA). In the second stage, by using the recovered sum-of-codewords as side information, the receiver recovers one of the two codewords using a modified SPA, ultimately recovering both codewords. The main benefit of recovering the sum-of-codewords instead of the codeword itself is that it allows to attain points on the dominant face of the multiple access channel capacity without the need of rate-splitting or time sharing while maintaining a low complexity in the order of a standard point-to-point decoder. This property is also shown to be crucial for some applications, e.g., interference channels. For all the simulations with single-layer binary codes, our proposed practical strategy is shown to be within \SI{1.7}{\decibel} of the theoretical limits, without explicit optimization on the off-the-self LDPC codes.

cs.IT↗