Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes

Malek Ellouze (1) , Romain Tajan (1) , Camille Leroux (1) , Christophe Jégo (1) , Charly Poulliat (2, 3, 4)

1 Bordeaux INP - Institut Polytechnique de Bordeaux
2 IRIT - Institut de recherche en informatique de Toulouse
3 Toulouse INP - Institut National Polytechnique (Toulouse)
4 IRIT-SC - Signal et Communications

In this paper, we present a deterministic algorithm to count the low-weight codewords of punctured and shortened pure and pre-transformed polar codes. The method first evaluates the weight properties of punctured/shortened polar cosets. Then, a method that discards the cosets that have no impact on the computation of the low-weight codewords is introduced.

A key advantage of this method is its applicability, regardless of the frozen bit set, puncturing/shortening pattern, or pretransformation. Results confirm the method's efficiency while showing reduced computational complexity compared to stateof-the-art algorithms.

Domaines: Théorie de l'information [cs.IT]

Malek Ellouze, Romain Tajan, Camille Leroux, Christophe Jégo, Charly Poulliat. Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes. 2024. ⟨hal-04770530v2⟩