Baseband Line Codes Via Spectral Factorization

We describe a method of designing baseband line codes with prescribed spectral nulls in the transmitted spectrum. These codes have the important property that the transmitted power is adjustable (with a concomitant change in spectral shape, i.e., null width) and can be made arbitrarily close to the innovations power, while keeping the minimum distance between signal points (or sequences) constant. The method is a generalization of the approach introduced by Forney and Calderbank [7] that discusses a spectral null at dc. We apply results from linear prediction theory; the essential design step requires the spectral factorization of a certain trigonometric polynomial. The line code that results can easily be used in conjunction with a large class of trellis coded modulation schemes (just as in [7]). In the second part of the paper, we construct specific baseband codes using a representation of the general theory that involves a dither variable, which is used to create integer symbols and to minimize the size of the symbol alphabet. We emphasize the design of line codes with a double null at dc employing the symbol alphabet {±1, ±3}. © 1989 IEEE

Duke Scholars

Author Robert Calderbank Computer Science