138 citations · 186 across the 16 of their papers we have counts for
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A Tutorial on Weight Structure of Polar Codes
Mohamamd Rowshan, Vlad-Florin Dragoi
This tutorial introduces the algebraic foundations underlying the weight structure of polar codes. Using a monomial-based polynomial formalism, we explain how polar and Reed-Muller…
A Hybrid Reliability--Weight Framework for Construction of Polar Codes
Mohammad Rowshan, Vlad-Florin Dragoi
Polar codes are usually constructed by ranking synthetic bit-channels according to reliability, which guarantees capacity-achieving behavior but can yield poor low-weight spectra a…
Generalized Weight Structure of Polar Codes: Selected Template Polynomials
Mohammad Rowshan, Vlad-Florin Dragoi
Polar codes can be viewed as decreasing monomial codes, revealing a rich algebraic structure governed by the lower-triangular affine (LTA) group. We develop a general framework to…
Algebraic Properties of PAC Codes
Vlad-Florin Dragoi, Mohammad Rowshan
We analyze polarization-adjusted convolutional codes using the algebraic representation of polar and Reed-Muller codes. We define a large class of codes, called generalized polynom…
Towards Weight Distribution-Aware Polar Codes
Mohammad Rowshan, Vlad-Florin Dragoi
Polar codes are constructed based on the reliability of sub-channels resulting from the polarization effect. However, this information-theoretic construction approach leads to a po…
On Weight Enumeration and Structure Characterization of Polar Codes via Group Actions
Vlad-Florin Dragoi, Mohammad Rowshan
In this article, we provide a complete characterization of codewords in polar codes with weights less than twice the minimum distance, using the group action of the lower triangula…
Weight Structure of Low/High-Rate Polar Codes and Its Applications
Mohammad Rowshan, Vlad-Florin Drăgoi, Jinhong Yuan
The structure of a linear block code is pivotal in defining fundamental properties, particularly weight distribution, and code design. In this study, we characterize the Type II st…
On the Closed-form Weight Enumeration of Polar Codes: 1.5-weight Codewords
Mohammad Rowshan, Vlad-Florin Drăgoi, Jinhong Yuan
The weight distribution of error correction codes is a critical determinant of their error-correcting performance, making enumeration of utmost importance. In the case of polar cod…
Fast Methods for Ranking Synthetic BECs
Hsin-Po Wang, Vlad-Florin Drăgoi
We gather existing methods that are used to compare and rank the BECs synthesized by a polar code constructor, compare them, and propose new methods that compare synthetic BECs fas…
Generalized Inverse Based Decoding
Ferucio Laurentiu Tiplea, Vlad-Florin Dragoi
The concept of Generalized Inverse based Decoding (GID) is introduced, as an algebraic framework for the syndrome decoding problem (SDP) and low weight codeword problem (LWP). The…
Bhattacharyya parameter of monomials codes for the Binary Erasure Channel: from pointwise to average reliability
Vlad-Florin Dragoi, Gabriela Cristescu
Monomial codes were recently equipped with partial order relations, fact that allowed researchers to discover structural properties and efficient algorithm for constructing polar c…
Algebraic Properties of Polar Codes From a New Polynomial Formalism
Magali Bardet, Vlad Dragoi, Ayoub Otmani +1
Polar codes form a very powerful family of codes with a low complexity decoding algorithm that attain many information theoretic limits in error correction and source coding. These…