Abstract
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.
Highlights
Nonlinear feedback shift registers (NFSRs) are the main building blocks in many convolutional decoders
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
Summary
Nonlinear feedback shift registers (NFSRs) are the main building blocks in many convolutional decoders. Some studies have focused on the stability of NFSRs. In 1964, Massey and Liu [1] proposed that using a stable nonlinear feedback shift register (NFSR) as the main building block in a convolutional decoder is able to limit such an error propagation. In 1964, Massey and Liu [1] proposed that using a stable nonlinear feedback shift register (NFSR) as the main building block in a convolutional decoder is able to limit such an error propagation In their NFSRbased decoder, the feedback function represents a decoding algorithm. We study the stability of multi-valued NFSRs using a logic network approach. Based on its logic network representation, we give the state transition matrix [34], which shows the simple relation with the truth table of the feedback function of the NFSR.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have