Maximum Spread of D-dimensional Multiple Turbo Codes

Emmanuel Boutillon (1) , David Gnaedig (1)

1 LESTER - Laboratoire d'Electronique des Systèmes TEmps Réel

This paper presents the mathematical framework involved in the determination of an upper bound of the maximum spread value of a D-dimensional Turbo-Code of frame size N. This bound is named Sphere Bound (SB). The SB is obtained using simple properties of the Euclidian space (sphere packing in a finite volume). The SB obtained for dimension 2 is equal to sqrt(2N). This result has already been conjectured. For dimension 3, we prove that the SB can not be reached, but closely approached (at least up to 95 %). For dimensions 4, 5 and 6, the construction of particular interleavers shows that SB can be approached up to 80 %. Moreover, we derive an asymptotic upper bound of the minimum Hamming weight of the weigth-two input sequence from the SB calculation.

Mots clés: Turbo-code; spead; sphere bound; multiple turbo-code

Domaines: Electronique

Emmanuel Boutillon, David Gnaedig. Maximum Spread of D-dimensional Multiple Turbo Codes. IEEE Transactions on Communications, 2005, 53 (8), pp.1237 - 1242. ⟨hal-00348121⟩