Computing the minimum distance of linear codes by the error impulse method.

Claude Berrou (1) , Sandrine Vaton (2, 3) , Michel Jezequel (1) , Catherine Douillard (4, 1)

1 ELEC - Département Electronique
2 INFO - Département informatique
3 LIT - Laboratoire Informatique et Télécommunications
4 IMT Atlantique - ELEC - Département Electronique

A new method for computing the minimum distances of linear error-correcting codes is proposed and justified. Unlike classical techniques that rely on exhaustive or partial enumeration of codewords, this new method is based on the ability of the Soft-In decoder to overcome Error Impulse input patterns. It is shown that the maximum magnitude of the Error Impulse that can be corrected by the decoder is directly related to the minimum distance. This leads to a very fast algorithm to obtain minimum distances of any linear code whatever the block size and the code rate considered. In particular, the method can be advantageously worked out for turbo-like concatenated codes.

Mots clés: Minimum distance; Error floor; Linear code; Convolutional code; Concatenated code; Turbo code

Domaines: Interface homme-machine [cs.HC]; Réseaux et télécommunications [cs.NI]; Electronique; Traitement du signal et de l'image [eess.SP]

Claude Berrou, Sandrine Vaton, Michel Jezequel, Catherine Douillard. Computing the minimum distance of linear codes by the error impulse method.. GLOBECOM '02 : IEEE GLOBECOM 2002, Nov 2002, Taipei, Taiwan. ⟨10.1109/GLOCOM.2002.1188348⟩. ⟨hal-01810157⟩