Parallel Generation of l-Sequences

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.