Low-Complexity Algorithm for the Minimum Distance Properties of PAC Codes
Malek Ellouze, Romain Tajan, Camille Leroux, Christophe Jégo, Charly Poulliat
Abstract
In this paper, a low-complexity algorithm that enables to compute the minimum distance as well as its associated number of occurrences for PAC codes is described. The method relies on the computation of the minimum weight properties of polar cosets while taking into consideration the initial precoding. Due to the exponential rise of the number of cosets, we propose a method that discards the cosets that have no impact on the computation of the minimum distance. This method does not impose any specific rules on the choice of the frozen bit set and the initial precoding.
Topics & Concepts
CosetComputationAlgorithmPrecodingComputer scienceSet (abstract data type)Computational complexity theoryMathematicsMIMOTelecommunicationsDiscrete mathematicsProgramming languageChannel (broadcasting)Error Correcting Code TechniquesAdvanced Wireless Communication TechniquesCoding theory and cryptography