Parallel Generation of l-Sequences

Abstract

The generation of pseudo-random sequences at a high rate is 
an important issue in modern communication schemes. The 
representation of a sequence can be scaled by decimation 
to obtain parallelism and more precisely a sub-sequences generator. 
Sub-sequences generators and therefore decimation have been 
extensively used in the past for linear feedback shift 
registers (LFSRs). However, the case of automata with a non 
linear feedback is still in suspend. In this work, we have studied 
how to transform of a feedback with carry shift register (FCSR) into a 
sub-sequences generator. We examine two solutions for this 
transformation, one based on the decimation properties of $ell$-sequences, 
extit{i.e.} FCSR sequences with maximal period, and the other one based 
on multiple steps implementation. 
We show that the solution based on the decimation properties leads to much 
more costly results than in the case of LFSRs. For the multiple steps 
implementation, we show how the propagation of carries affects the design.
par This work represents a cooperation with Cédric Lauradoux and was
presented at the international conference on SEquences and Their
Applications (SETA) 2008.