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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…