Optimization of signal sets for partial-response channels. II. Asymptotic coding gain

For Pt. I see ibid., vol.37, no.5, p.1327-141 (1991). For a linear, time-invariant, discrete-time channel with a given transfer function H(f), and information rate R bits/ T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2^RK inputs of length K that maximizes the minimum l₂ distance between pairs of outputs. The author studies the minimum distance between outputs, or equivalently, the coding gain of optimal signal sets as K→∞. He shows how to estimate the coding gain, relative to single-step detection, of an optimal signal set length K when K is large