On Stability of Multi-Valued Nonlinear Feedback Shift Registers

Abstract EN

Nonlinear feedback shift registers (NFSRs) are the main building blocks in many convolutional decoders, and a stable NFSR can limit decoding error propagation.

Due to lack of efficient algebraic tools, the stability of multi-valued NFSRs has been much less studied.

This paper studies the stability of multi-valued NFSRs using a logic network approach.

A multi-valued NFSR can be viewed as a logic network.

Based on its logic network representation, some sufficient and necessary conditions are provided for globally (locally) stable multi-valued NFSRs, explicit forms are given for the set of basins, and the algorithm for obtaining the set of basins is provided as well.

Finally, a new method is presented for constructing stable n+1-stage NFSRs from stable n-stage NFSRs by the properties of D-morphism.