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A new method for evaluating the power spectral density of multitrack constrained sequences is demonstrated for multitrack (0, G/I) constraints. (0, G/I) constrained sequences are used in magnetic recording systems that employ partial response maximum likelihood (PRML) signalling. Using the proposed approach, the number of states in a directed graph representing the given (0, G/I) constraint is reduced remarkably so that the power spectral density can be easily calculated.

A new method of spectral analysis for coded sequences is introduced. An autocorrelation function is expressed by a system of difference equations. A translation of the system into the frequency domain by a z transform enables an expression for a code spectrum to be obtained after a few simple algebraic transformations. As an example the HDBn code spectrum is evaluated.

A scrambling method for nonequiprobable signalling is proposed. This method uses a lossless compression decoder to produce symbols with unequal probabilities. The relative symbol frequencies and correlation characteristics are calculated and the noisy channel error performance is discussed. In one application of this nonequiprobable signalling procedure it is shown that 0.68 dB of a possible 1.53 dB gain is easily obtained for signal constellation shaping applications.