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AMC

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.
AMC

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.

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