On cycle-free lattices with high rate label codes
Amin Sakzad Mohammad-Reza Sadeghi
Advances in Mathematics of Communications 2010, 4(4): 441-452 doi: 10.3934/amc.2010.4.441
Etzion et al. have shown that high rate codes based on cycle-free Tanner graphs have minimum distance at most $2$. This result was extended by Sadeghi et al. to a small class of lattices based on Construction $D'$ only. In this paper, we prove a key theorem which relates the minimum distance of every lattice to the minimum distance of its label code. Then, using this powerful tool along with some new bounds on minimum distance of cycle-free group codes, we generalize those results to a large class of lattices here called RPS and PFP lattices. More importantly, we show that this class of cycle-free lattices are not so good in the view of coding gain.
keywords: group code Tanner graph label code. Lattice
Cycle structure of permutation functions over finite fields and their applications
Amin Sakzad Mohammad-Reza Sadeghi Daniel Panario
Advances in Mathematics of Communications 2012, 6(3): 347-361 doi: 10.3934/amc.2012.6.347
In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field $\mathbb F_q$. For the first time Möbius and Rédei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of Rédei functions an exact formula for the inverse function is derived. The cycle structure of Rédei functions is also investigated. The self-inverse and non-self-inverse versions of these permutation functions can be used to construct new interleavers.
keywords: Interleavers and permutation functions over finite fields.

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