Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1111.6828

Bayesian Estimation of a Gaussian source in Middleton's Class-A Impulsive Noise

Paolo Banelli
View original source ↗Read source document ↗Export metadata ↓

Abstract

The paper focuses on minimum mean square error (MMSE) Bayesian estimation for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. In addition to the optimal Bayesian estimator, the paper considers also the soft-limiter and the blanker, which are two popular suboptimal estimators characterized by very low complexity. The MMSE-optimum thresholds for such suboptimal estimators are obtained by practical iterative algorithms with fast convergence. The paper derives also the optimal thresholds according to a maximum-SNR (MSNR) criterion, and establishes connections with the MMSE criterion. Furthermore, closed form analytic expressions are derived for the MSE and the SNR of all the suboptimal estimators, which perfectly match simulation results. Noteworthy, these results can be applied to characterize the receiving performance of any multicarrier system impaired by a Gaussian-mixture noise, such as asymmetric digital subscriber lines (ADSL) and power-line communications (PLC).

Explore related subjects

cs.ITmath.ITstat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Paolo Banelli. 2012-12-11. Bayesian Estimation of a Gaussian source in Middleton's Class-A Impulsive Noise. https://doi.org/10.1109/lsp.2013.2274774

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Large Language Models As Shannon Lossy Compressors Not Solomonoff Induction Estimators: The Singularity Is Not Near Without Symbolic Model Synthesis in Program Space

On the one hand, the question of whether Large Language Models (LLMs) are Solomonoff induction estimators has become an explicit question at the intersection of Algorithmic Information Theory (AIT) and Machine Learning (ML) of great interest. On the other hand, the now old idea of an AI Singularity that requires a reliable positive-feedback process in which a system can generate, evaluate and retain genuine improvements to itself continues to come up and is a recurrent concept in the discussion of AGI. We connect and provide some answers to these issues based on current assumptions and future developments of neurosymbolic ML. We will demonstrate that cross-entropy, negative log-likelihood and cognate next-token objectives do not or cannot, by themselves, implement Solomonoff induction: they optimise fit to a supplied conditional distribution rather than a program-weighted universal mixture. While more compute within a fixed objective can improve fit without changing the inductive principle, additional computational resources do not intrinsically without external hyper-parameter or architectural changes, behave as optimal predictors in the Solomonoff and Levin sense. While the data-processing inequality (DPI) and Levin non-growth remain valid, we will show that for finite learners and finite observers, theoretical boundaries have less relevancy and generate a drift between possible approaches. To this end, we interpret different resource-bounded estimators as finite tools for mechanism search that show divergence, not violation, of (algorithmic) information conservation laws. A neurosymbolic direction taken by current frontier-model developers points towards the adoption of model synthesis and no longer purely statistical approaches to LLMs but where Solomonoff estimators are possible.

cs.IT↗
arXiv2026

Sensing-Aided Secure Multicast in Rotatable Antenna-Enabled ISAC Systems

Acquiring the channel state information (CSI) of passive eavesdroppers remains a fundamental challenge in physical layer security. The sensing capability of integrated sensing and communication (ISAC) systems enables estimation of a potential eavesdropper's angle of departure (AoD) before secure transmission. Accordingly, a sensing-aided secure multicast scheme is proposed using a rotatable antenna (RA) architecture that combines array-level and element-level rotations with analog beamforming. The scheme comprises eavesdropper sensing and secure communication stages. In the sensing stage, the maximum likelihood estimator (MLE) and corresponding Cramer--Rao bound (CRB) are derived for eavesdropper AoD estimation. The two rotation levels are then optimized through cyclic coordinate search to minimize the worst-case CRB. The resulting AoD estimate and CRB determine the center and width of the angular uncertainty region, respectively. In the communication stage, the constant-modulus analog beamformer and RA configuration are jointly optimized to maximize the worst-case secrecy rate over this region. After angular discretization and smooth approximation, the resulting problem is solved using a product-space joint optimization framework. Numerical simulation results validate the convergence and effectiveness of the proposed algorithms. It is demonstrated that i) the proposed RA-enabled sensing design effectively improves the eavesdropper AoD estimation accuracy; ii) a high and nearly constant secrecy rate is maintained over the uncertainty region; and iii) the joint optimization of the two rotation levels yields lower CRBs and higher secrecy rates than schemes employing either a fixed-position array or a single rotation level.

cs.IT↗
arXiv2026

Successive Refinement Under Strong-Sense Perfect Perception

We revisit a multiterminal lossy source coding problem named successive refinement and derive the rate-distortion-perception region under the strong-sense perfect perception constraint in the presence of unlimited common randomness. Specifically, in successive refinement, one aims to compress a source sequence and allows two distinct decoders to recover the source sequence at different distortion levels. By imposing the strong-sense perfect perception constraint, our results refine the previous result by analyzing the impact of the perceptual quality. Our achievability proof is inspired by output constrained lossy source coding and our converse proof adapts the proof steps of the standard successive refinement problem. Furthermore, we provide a numerical example of the Bernoulli source to illustrate our result and show that the Bernoulli source under Hamming distortion is successively refinable even with the strong-sense perfect perception constraint.

cs.IT↗