Channels leading to rapid error recovery for decision feedback equalizers

The authors define the DFE (decision feedback equalizer) system of interest and their finite-error-recovery-time problem. They present their basic result, which establishes that whenever the channel satisfies a simple frequency-domain constraint, the error recovery time of an ideal DFE is always finite. They also include four applications of this theorem, including analysis of a real channel. Convergence rates and explicit bounds, given an exponential overbound on the channel impulse response, are presented. Results of greater practical interest, where the authors relax most of the major idealized assumptions, are also given. The authors present the result for M-ary data and relate the error recovery time bound back to the binary case. A formula for the error probability, given a high signal-to-noise-ratio channel, is provided