Revisiting zero-rate bounds on the reliability function of discrete memoryless channels
share
We present a new proof of Berlekamp's zero-rate upper bound on the reliability function of discrete memoryless channels, in its extended form for list-decoding as first proved by Blinovsky. The Berlekamp-Blinovsky proof, which is the only one available in the literature, is based on a rather unusual procedure which prevents the combination with other tools for possible extensions of the result. We present a proof that - we think - is more transparent and more convenient to play with. The main ideas and tools used are not new and our aim is indeed to give a standardized proof based on well established and reusable principles. An important part, namely the use of Ramsey theory and of a beautiful result by Komlos, was already considered by Blinovsky himself for a similar problem of packing in Hamming spaces. However, we use some variations and combinations with other tools which lead, in our opinion, to a cleaner proof also for this specific problem. To the best of our knowledge, this was never presented before.
READ FULL TEXT