High-order spectral -null multimode code

Constrained codes are employed in digital magnetic and optical storage systems to ensure that the recorded signals match the characteristics of the recoding channels to improve system performance. This thesis introduces a new class of constrained codes, high-order spectral-null multimode codes.;First, characteristics of high-order spectral-null codes are summarized, and further characteristics of these codes are investigated. A new method for enumerating codewords with specified values of word-end disparity and word-end disparity sum is introduced. These codewords are of interest for the design of second-order spectral-null codes. Enumeration rules are given, and two new efficient algorithms for evaluating the cardinality of codewords based on this enumeration method are derived. Calculation results demonstrate the advantages of the new enumeration algorithms.;Evaluation of power spectra of fixed-length and variable-length codes is then reviewed. This thesis demonstrates that sum variance, a performance metric for first-order spectral-null codes, cannot be generalized to be a valid metric for higher-order spectral-null codes and proposes a new performance metric, low-frequency spectrum-weight, for evaluation of an arbitrary high-order spectral-null code. It is shown that the asymptotic low-frequency spectral components of high-order spectral-null codes are exclusively determined by the order of spectral null and the low-frequency spectrum-weight. Low-frequency spectrum-weight of state-dependent and state-independent codes, and fixed-length and variable-length high-order spectral-null codes is evaluated. Several closed-from expressions are derived for the low-frequency spectrum-weight of specific classes of codes.;A state-dependent encoding method is proposed to construct rate-efficient high-order spectral-null bimode and multimode codes. The guided scrambling multimode coding technique is summarized, and a new serial encoder structure is proposed. Necessary and sufficient conditions for the generation of complementary quotients in each guided scrambling selection set are derived. Scrambling polynomials suitable for implementation of high-order spectral-null multimode codes are obtained through further computer search.;The analysis of low-frequency spectrum-weight of the equivalent state-independent variable-length encoder provides insight into the construction of good fixed-length high-order spectral-null codes as well as good first-order spectral-null codes with a large rejection of spectral components at low frequencies. Spectral results of various high-order spectral-null multimode codes introduced in this thesis demonstrate that the new codes can yield superior spectral performance and higher rate codes than other high-order spectral-null codes developed to date.