Analysis of Linear Huffman Filters under Arbitrary Initial Conditions

A mathematical description is formulated for the operation of Huffman filters under any initial conditions in the nonautonomous and autonomous regimes. Methods are given for solving inhomogeneous difference equations over the field $GF(2)$ as well as for calculating the sequence at the output of any section, null sequences, and code rings of type $A$. The dependence of the period of an autonomous sequence on the divisibility of the initial-state polynomial and the truncated characteristic polynomial is determined. The sequential connection of and equivalence conditions for filters are discussed, along with filters of general form, correction of the state vector, etc.