On the spectral characteristics of continuous guided scrambling line codes

Line codes are used in digital communication systems to control the characteristics of transmitted symbol sequences. Recently, an efficient and easily implemented family of codes called guided scrambling (GS) codes has been introduced. Previous work indicated that continuous GS (CGS) codes can be configured to generate encoded sequences with statistics nearly independent from those of the source bit stream, a property not available with any other efficient line code technique developed to date. This paper presents analysis of the spectral characteristics of these codes which confirms this conjecture. The principle of guided scrambling is reviewed. Then, by showing that the scrambling polynomials currently recommended for GS codes can be regarded as base polynomials for large families of polynomials, expanded sets of scrambling polynomials are proposed. Evaluation of the power spectral density of CGS codes which use scrambling polynomials from these expanded sets is then considered, under the condition only that the input bit stream is stationary. Expressions which limit required computation to practical limits are developed, and results for several code configurations are given. Here it is demonstrated that when scrambling polynomials of high degree are used, the characteristics of the transmitted symbol sequence become nearly independent of the source bit stream statistics