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Maximally null partial response for an MLSE digital data system involving high loss coaxial cable

Digital data systems are considered in which reception is based on the principle of maximum-likelihood sequence estimation (MLSE) and in which the channel has the coaxial cable power transfer characteristic e^{-\alpha \mid \omega \mid ^{1/2} } . When only the average transmitter output power and the response memory ( \nu ) are constrained, it is shown that, as \alpha increases, the optimal overall system impulse response tends to a partial response for which the corresponding frequency characteristic is proportional to the unique normalized trigonometric polynomial having \nu th order zeros at the Nyquist bandlimits. These same partial responses result if \alpha is fixed and the band rate is increased. This observation helps explain a recent numerical study by Fredricsson that has stirred wide-spread interest. The minimum distance associated with such an optimal response is tabulated for various values of \nu and various numbers of levels.