arXiv subjects

Chloe Makdad

Publications and source records attributed to Chloe Makdad.

5 recordsLinked to original sources

arXiv2026

Two-Level Decorrelated Coded Modulation on the $D_4$ Lattice

We propose \textit{two-level decorrelated coding} (TLDC), a novel coded modulation scheme for the $D_4$ lattice that combines Voronoi shaping with a two-stage decoding process to achieve lattice shaping and coding gains at low complexity. In TLDC, the decoded values of the first level allow the several random variables in the second level to become approximately uncorrelated. The resulting independence of the variables in level two permits decoding in parallel or consolidation into a larger codeword, enhancing performance. TLDC supports flexible choice of FEC within each level. Using bit-interleaved or multi-level polar codes at each level, the resulting coded modulation scheme exhibits a gain of up to 0.5 dB over analogous state-of-the-art coded modulation schemes on a 16-QAM under AWGN at block sizes of 64 and 1024 bits.

cs.IT↗

arXiv2026

Ray-Tracing vs. 3GPP TDL: Power Delay Profile Analysis in Outdoor-to-Indoor and Indoor Channels

3rd Generation Partnership Project (3GPP) Technical Report (TR) 38.901 channel models (Releases 15-19) are widely used for physical-layer design and system-level evaluation in dense urban outdoor-to-indoor (O2I) and indoor environments. These models capture ensemble-averaged channel statistics but do not account for site-specific geometry. In this paper, we compare Power Delay Profiles (PDPs) derived from a deterministic ray-tracing model (Remcom Wireless InSite software) with those from the 3GPP TR 38.901 Tapped Delay Line (TDL) channel models. This comparative analysis is performed using a dense urban O2I scenario and a representative single-story indoor layout modeled in Washington, D.C., under matched link-distance and Non-Line-of-Sight (NLOS) conditions. All Wireless InSite PDPs are power-normalized to enable comparison of relative multipath delay structure. We evaluate root-mean-square (RMS) delay spread, mean excess delay, effective maximum delay, and Kullback-Leibler (KL) distribution divergence. Results indicate that 3GPP TDL models generally exhibit longer delay spreads and often fail to capture deterministic, site-specific features such as late-arriving energy and irregular spikes. While TDL models can approximate primary channel features in some cases, their reliance on ensemble-averaged statistics rather than geometry limits their representation of fine multipath structures. We conclude that while 3GPP TDL models are suitable for large-scale system evaluation, deterministic or hybrid approaches are more appropriate for site-specific physical-layer design.

eess.SP↗

arXiv2026

Multilevel Coset Codes on Lattices

This work introduces coset Bombe codes, a novel class of multilevel coset codes that generalize polar codes to dense lattice structures. By leveraging multilevel coding with non-binary codes designed for the lattice modulations and making use of Voronoi shaping, Bombe codes integrate the geometric strengths of dense lattices such as $D_4$ with the capacity-approaching properties of polar codes. Experimental results in additive white Gaussian noise (AWGN) channels demonstrate that coset Bombe codes significantly outperform both BICM and MLC state-of-the-art schemes on 16-QAM. The proposed scheme simulated on AWGN achieves up to 0.8 dB of gain and reduces block size latency by half while maintaining superior bit and block error rate (BER/BLER) performance on codewords of 256 and 1024 bits.

cs.IT↗

arXiv2022

An Algorithm for Ennola's Second Theorem and Counting Smooth Numbers in Practice

Let $Ψ(x,y)$ count the number of positive integers $n\le x$ such that every prime divisor of $n$ is at most $y$. Given inputs $x$ and $y$, what is the best way to estimate $Ψ(x,y)$? We address this problem in three ways: with a new algorithm to estimate $Ψ(x,y)$, with a performance improvement to an established algorithm, and with empirically based advice on how to choose an algorithm to estimate $Ψ$ for the given inputs. Our new algorithm to estimate $Ψ(x,y)$ is based on Ennola's second theorem [Ennola69], which applies when $y< (\log x)^{3/4-ε}$ for $ε>0$. It takes $O(y^2/\log y)$ arithmetic operations of precomputation and $O(y\log y)$ operations per evaluation of $Ψ$. We show how to speed up Algorithm HT, which is based on the saddle-point method of Hildebrand and Tenenbaum [1986], by a factor proportional to $\log\log x$, by applying Newton's method in a new way. And finally we give our empirical advice based on five algorithms to compute estimates for $Ψ(x,y)$.The challenge here is that the boundaries of the ranges of applicability, as given in theorems, often include unknown constants or small values of $ε>0$, for example, that cannot be programmed directly.

math.NT↗

arXiv2020

Accelerating the Distributed Kaczmarz Algorithm by Strong Over-relaxation

The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz algorithm to the situation in which data is distributed throughout a network represented by a tree. We isolate substructures of the network and study convergence of the distributed Kazmarz algorithm for relatively large relaxation parameters associated to these substructures. If the system is consistent, then the algorithm converges to the solution of minimal norm; however, if the system is inconsistent, then the algorithm converges to an approximated least-squares solution that is dependent on the parameters and the network topology. We show that the relaxation parameters may be larger than the standard upper-bound in literature in this context and provide numerical experiments to support our results.

math.NA↗