arXiv subjects

Samin Riasat

Publications and source records attributed to Samin Riasat.

8 recordsLinked to original sources

arXiv2026

Precoding Design for Limited-Feedback MIMO Systems via Character-Polynomial Codes

This paper presents a precoding codebook design for limited-feedback multiple-input multiple-output (MIMO) systems under the equal-gain transmission (EGT) constraint. In particular, we demonstrate that character--polynomial (CP) codes provide a structured solution that achieves constant-envelope transmission, low storage complexity, and Grassmannian packing without dependence on array geometry or channel statistics. In contrast to geometry-dependent discrete Fourier transform (DFT) codebooks used in current 5G systems and unstructured Grassmannian codebooks with high storage complexity, CP codebooks combine practical implementation advantages with near-optimal packing performance. For multiple-input single-output (MISO) systems, we derive an upper bound on the mean squared quantization error and show that the distortion relative to the EGT baseline vanishes asymptotically as the number of transmit antennas increases and the code rate approaches one. For MIMO systems with two receive antennas, we develop an iterative method to establish the EGT baseline. Simulation results under Rayleigh, correlated, and clustered delay line (CDL) channel models show that CP codebooks approach the EGT baseline across all channel conditions while outperforming phase shift keying (PSK) and 5G DFT codebooks in several operating regimes, and, in the Rayleigh fading case, incur negligible packing loss relative to numerically optimized Grassmannian codebooks obtained via the alternating projection (AP) method.

eess.SP↗

arXiv2026

Covering in Hamming and Grassmann Spaces: New Bounds and Reed--Solomon-Based Constructions

We study covering problems in Hamming and Grassmann spaces through a unified coding-theoretic and information-theoretic framework. Viewing covering as a form of quantization in general metric spaces, we introduce the notion of the average covering radius as a natural measure of average distortion, complementing the classical worst-case covering radius. By leveraging tools from one-shot rate-distortion theory, we derive explicit non-asymptotic random-coding bounds on the average covering radius in both spaces, which serve as fundamental performance benchmarks. On the construction side, we develop efficient puncturing-based covering algorithms for generalized Reed--Solomon (GRS) codes in the Hamming space and extend them to a new family of subspace codes, termed character-Reed--Solomon (CRS) codes, for Grassmannian quantization under the chordal distance. Our results reveal that, despite poor worst-case covering guarantees, these structured codes exhibit strong average covering performance. In particular, numerical results in the Hamming space demonstrate that RS-based constructions often outperform random codebooks in terms of average covering radius. In the one-dimensional Grassmann space, we numerically show that CRS codes over prime fields asymptotically achieve average covering radii within a constant factor of the random-coding bound in the high-rate regime. Together, these results provide new insights into the role of algebraic structure in covering problems and high-dimensional quantization.

cs.IT↗

arXiv2025

Efficient Covering Using Reed--Solomon Codes

We propose an efficient algorithm to find a Reed-Solomon (RS) codeword at a distance within the covering radius of the code from any point in its ambient Hamming space. To the best of the authors' knowledge, this is the first attempt of its kind to solve the covering problem for RS codes. The proposed algorithm leverages off-the-shelf decoding methods for RS codes, including the Berlekamp-Welch algorithm for unique decoding and the Guruswami-Sudan algorithm for list decoding. We also present theoretical and numerical results on the capabilities of the proposed algorithm and, in particular, the average covering radius resulting from it. Our numerical results suggest that the overlapping Hamming spheres of radius close to the Guruswami-Sudan decoding radius centered at the codewords cover most of the ambient Hamming space.

cs.IT↗

arXiv2024

Decoding Analog Subspace Codes: Algorithms for Character-Polynomial Codes

We propose efficient minimum-distance decoding and list-decoding algorithms for a certain class of analog subspace codes, referred to as character-polynomial (CP) codes, recently introduced by Soleymani and the second author. In particular, a CP code without its character can be viewed as a subcode of a Reed-Solomon (RS) code, where a certain subset of the coefficients of the message polynomial is set to zeros. We then demonstrate how classical decoding methods, including list decoders, for RS codes can be leveraged for decoding CP codes. For instance, it is shown that, in almost all cases, the list decoder behaves as a unique decoder. We also present a probabilistic analysis of the improvements in list decoding of CP codes when leveraging their certain structure as subcodes of RS codes.

cs.IT↗

arXiv2022

Quotients of Palindromic and Antipalindromic Numbers

A natural number N is said to be palindromic if its binary representation reads the same forwards and backwards. In this paper we study the quotients of two palindromic numbers and answer some basic questions about the resulting sets of integers and rational numbers. For example, we show that the following problem is algorithmically decidable: given an integer N, determine if we can write N = A/B for palindromic numbers A and B. Given that N is representable, we find a bound on the size of the numerator of the smallest representation. We prove that the set of unrepresentable integers has positive density in N. We also obtain similar results for quotients of antipalindromic numbers (those for which the first half of the binary representation is the reverse complement of the second half). We also provide examples, numerical data, and a number of intriguing conjectures and open problems.

math.NT↗

arXiv2020

New Bounds on Antipowers in Words

Fici et al. defined a word to be a k-power if it is the concatenation of k consecutive identical blocks, and an r-antipower if it is the concatenation of r pairwise distinct blocks of the same size. They defined N (k, r) as the smallest l such that every binary word of length l contains either a k-power or an r-antipower. In this note we obtain some new upper and lower bounds on N (k, r). We also consider avoiding 3-antipowers and 4-antipowers over larger alphabets, and obtain a lower bound for N (k, 5) in the binary case.

cs.FL↗

arXiv2018

Infinite products involving binary digit sums

Let $(u_n)_{n\ge 0}$ denote the Thue-Morse sequence with values $\pm 1$. The Woods-Robbins identity below and several of its generalisations are well-known in the literature \begin{equation*}\label{WR}\prod_{n=0}^\infty\left(\frac{2n+1}{2n+2}\right)^{u_n}=\frac{1}{\sqrt 2}.\end{equation*} No other such product involving a rational function in $n$ and the sequence $u_n$ seems to be known in closed form. To understand these products in detail we study the function \begin{equation*}f(b,c)=\prod_{n=1}^\infty\left(\frac{n+b}{n+c}\right)^{u_n}.\end{equation*} We prove some analytical properties of $f$. We also obtain some new identities similar to the Woods-Robbins product.

math.NT↗

arXiv2017

More Infinite Products: Thue-Morse and the Gamma function

Letting $(t_n)$ denote the Thue-Morse sequence with values $0, 1$, we note that the Woods-Robbins product $$ \prod_{n \geq 0} \left(\frac{2n+1}{2n+2}\right)^{(-1)^{t_n}} = 2^{-1/2} $$ involves a rational function in $n$ and the $\pm 1$ Thue-Morse sequence $((-1)^{t_n})_{n \geq 0}$. The purpose of this paper is twofold. On the one hand, we try to find other rational functions for which similar infinite products involving the $\pm 1$ Thue-Morse sequence have an expression in terms of known constants. On the other hand, we also try to find (possibly different) rational functions $R$ for which the infinite product $\prod R(n)^{t_n}$ also has an expression in terms of known constants.

math.NT↗