The Performance of Block Codes, Volume 49, Number 1

I n his classic 1948 paper [10], Claude Shannon introduced the notions of communication channels and codes to communicate over them. During the following two decades, he remained active in refining and extending the theory. One of Shannon’s favorite research topics was the fundamental performance capabilities of long block codes. In the 1950s and 1960s this topic also attracted the active involvement of several of Shannon’s distinguished colleagues both at Bell Telephone Laboratories and at MIT, including P. Elias, R. M. Fano, R. G. Gallager, E. N. Gilbert, R. W. Hamming, I. M. Jacobs, B. Reiffen, D. Slepian, and J. M. Wozencraft, and several graduate students, including G. D. Forney and me. The work culminated in a book by Gallager [6] and in a sequence of two “Information and Control” papers by Shannon, Gallager, and Berlekamp [11]. In this article I present an overview of some of the more salient results and their impact.