Guided Scrambling Polynomials for Periodic Quotient Relationship Patterns

Guided scrambling (GS) is a constrained coding technique that can be used in digital communication systems to control the characteristics of the encoded sequence. In each encoding interval, a GS encoder constructs a quotient selection set with a number of codeword candidates and selects the "best" candidate to represent the source word. Relationships between candidates in the quotient selection set impact the quality of the transmitted sequence. In particular, in some applications it is desired that the quotient relationship patterns (QRPs) be periodic, and in other applications, periodic QRPs are to be avoided. QRPs are determined by the scrambling polynomial. In this correspondence, we derive the general form for scrambling polynomials that generate all periodic quotient relationship patterns.