Channels leading to rapid error recovery for decision feedback equalizers: passivity analysis

When a decision feedback equalizer is used on a channel satisfying a simple constraint the error recovery time is bounded, and thus recovery is rapid, regardless of the initial conditions and the particular data sequence. The authors define the finite-error-recovery-time problem. The background passivity theory is then given along with the authors´ main theorem. Four applications are presented, including an analysis of a real channel. Convergence rates and explicit bounds are established, given an exponential overbound on the channel impulse response. The result for M-ary data is presented, and the error-recovery-time bound is related back to the binary case. For high SNR channels satisfying a passivity constraint, a formula for error probability is given