Properties of guided scrambling encoders and their coded sequences

Abstract

Guided scrambling (GS) line codes augment the source bit stream prior to self-synchronizing scrambling to ensure that the scrambling process generates an encoded bit sequence with good line code characteristics. With arithmetic from the ring of polynomials over GF(2), self-synchronizing scrambling can be interpreted as division of the source bit sequence by the scrambling polynomial and transmission of the resulting quotient. When augmenting bits are inserted in fixed, periodic positions, GS codes can be interpreted as block line codes which encode source words to quotients. In particular, block guided scrambling (BGS) generates a transmitted bit stream which is a concatenation of finite-length quotients chosen from sets of quotients which represent each source word. Alternatively, in continuous guided scrambling (CGS), the transmitted sequence appears to be a continuous quotient due to the fact that the encoder shift registers are updated following quotient selection to contain the remainder associated with the selected quotient. The quotient selection mechanisms of both BGS and CGS encoders can be modeled as finite state machines with quotient sets as input and the selected quotient as output. In CGS encoding, the selection mechanism also outputs the remainder associated with the selected quotient. In this paper we describe several characteristics of GS encoders and their coded sequences.