On codes satisfying Mth-order running digital sum constraints

Multi level sequences with a spectral null of order M at frequency f, meaning that the power spectral density, and its first 2M-1 derivatives vanish at f, are characterized by finite-state transition diagrams (FSTDs) whose edge labels satisfy bounds on the variation of the Mth-order running digital sum (RDS). Necessary and sufficient conditions for FSTDs with higher order null constraints at DC and at an arbitrary submultiple of the symbol frequency are derived. Analytical results are given concerning the performance of codes satisfying an Mth-order RDS constraint on partial-response channels. Specific code designs for quaternary channel inputs are presented. The Euclidean distance properties of this new class of codes, aside from their spectral-shaping properties, are demonstrated