Characteristics of guided scrambling encoders and their coded sequences

We derive several properties of guided scrambling (GS) encoders and the sequences they generate. We first highlight symmetrical aspects of the GS encoding mechanisms proposed to date, and then show that the existence of discrete components in the power spectrum of the pulse-amplitude-modulated encoded sequence can be predicted from the weight of the scrambling polynomial. We also show that with equiprobable source words, the block or continuous nature of the code has no effect on the statistics of the encoded sequence. We conclude by demonstrating how these properties simplify evaluation of the spectral characteristics of GS coded sequences