Spectrum Shaping with Alphabetic Codes with Finite Autocorrelation Sequence

In this paper we consider the problem of recoding binary data into ternary sequences for synchronous baseband data transmission systems. Our major objective is the shaping of the power spectral density of the channel process in order to combat the effects of intersymbol interference caused by the low-frequency cut-off of the channel. This motivates our interest in designing codes whose channel process has small Power in the low frequency range. Based on the MacLaurin expansion of the power density function, we use as a design heuristic the normalized second derivative Δ of the latter. To make computationally manageable the expression of Δ, we restrict ourselves to a class of codes whose autocorrelation sequence contains a finite number of nonzero terms, and present a corresponding code design algorithm. As examples, we exhibit two new codes which in many respects improve over the spectra of corresponding well-known codes.