Critique du rapport signal à bruit en communications numériques -- Questioning the signal to noise ratio in digital communications

Michel Fliess (1, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 ALIEN - Algebra for Digital Identification and Estimation

The signal to noise ratio, which plays such an important rôle in information theory, is shown to become pointless for digital communications where the demodulation is achieved via new fast estimation techniques. Operational calculus, differential algebra, noncommutative algebra and nonstandard analysis are the main mathematical tools.

Mots clés: Information theory; signal processing; digital communications; carriers; symbols; modulation; demodulation; noises; estimation; signal to noise ratio; operational calculus; noncommutative algebra; nonstandard analysis; differential algebra; nonstandard analysis.

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Anneaux et algèbres [math.RA]; Logique [math.LO]; Probabilités [math.PR]; Traitement du signal et de l'image [eess.SP]

Michel Fliess. Critique du rapport signal à bruit en communications numériques -- Questioning the signal to noise ratio in digital communications. Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, 2008, 2007 Conference in Honor of Claude Lobry, 9, pp.419-429. ⟨inria-00311719v1⟩