The relation between block length and reliability for a cascade of AWGN links

This paper presents a fundamental informationtheoretic scaling law for a heterogeneous cascade of links corrupted by Gaussian noise. For any set of fixed-rate encoding/decoding strategies applied at the links, it is claimed that a scaling of Θ(log n) in block length is both sufficient and necessary for reliable communication. A proof of this claim is provided using tools from the convergence theory for inhomogeneous Markov chains.