  In this paper we address the issue of pruning (i.e., shortening) a given
interleaver via truncation of the transposition vector of the mother
permutation and study its impact on the structural properties of the
permutation. This method of pruning allows for continuous un-interrupted data
flow regardless of the permutation length since the permutation engine is a
buffer whose leading element is swapped by other elements in the queue. The
principle goal of pruning is that of construction of variable length and hence
delay interleavers with application to iterative soft information processing
and concatenated codes, using the same structure (possibly in hardware) of the
interleaver and deinterleaver units. We address the issue of how pruning
impacts the spread of the permutation and also look at how pruning impacts
algebraically constructed permutations. We note that pruning via truncation of
the transposition vector of the permutation can have a catastrophic impact on
the permutation spread of algebraically constructed permutations. To remedy
this problem, we propose a novel lifting method whereby a subset of the points
in the permutation map leading to low spread of the pruned permutation are
identified and eliminated. Practical realization of this lifting is then
proposed via dummy symbol insertion in the input queue of the Finite State
Permuter (FSP), and subsequent removal of the dummy symbols at the FSP output.
