A revisitation of zero-rate bounds on the reliability function of discrete memoryless channels

We revise the proof of the zero-rate upper bounds on the reliability function of discrete memoryless channels for ordinary and list-decoding schemes. The available proofs devised by Berlekamp and Blinovsky are somehow uneasy in that they contain in one form or another some cumbersome "non-standard" procedures or computations. Here we follow Blinovsky's idea of using a Ramsey-theoretic result by Komlos, but we complement this with some missing steps to present a proof which is entirely in the realm of standard information theoretic tools even for general list size. We further add some comments on the connection between the two proofs to show that Berlekamp's and Komlos' results are essentially equivalent.