Key words: turbo codes, interleavers, spread, multiple turbo codes, sphere bound
Abstract: 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.
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Authors: Emmanuel Boutillon, David Gnaedig
Reference: IEEE Transactions on Communications, vol. 53, no. 8, aug. 2005