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Maximum Spread of D -Dimensional Multiple Turbo Codes

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2 Author(s)
Boutillon, E. ; LESTER, Univ. de Bretagne Sud, Lorient, France ; Gnaedig, D.

This letter 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 the sphere bound (SB). It is obtained using some simple properties of Euclidian space (sphere packing in a finite volume). The SB obtained for dimension 2 is equal to$sqrt2N$. This result has already been conjectured. For dimension 3, we prove that the SB cannot be reached, but can be closely approached (at least up to 95%). For dimensions 4–6, the construction of particular interleavers shows that the SB can be approached up to 80%. Moreover, from the SB calculation, an estimate of the minimum Hamming weight of the weight-two input sequence is derived.

Published in:

Communications, IEEE Transactions on  (Volume:53 ,  Issue: 8 )

Date of Publication:

Aug. 2005

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