Asymptotic optimality of finite-memory detection

The subject of this paper is the asymptotic optimality of finite-memory detection for transmission over a channel characterized by a single multiplicative time-invariant stochastic parameter (e.g., block frequency non-selective fading). It is known that any finite-memory detection algorithm, either trellis-based or graph-based, is characterized by a single basic metric. We present a theorem which proves that this metric tends, asymptotically, to that of a receiver with perfect channel state information.