New Identities for the Shannon Function with Applications
Aiden A. Bruen, Mario Professor Forcinito, James Professor McQuillan · 2021
This chapter illustrates the connections between the three subjects in the title of this book. Information theory tells us the bound. The identities suggest possibilities for constructing algorithms that come close to producing a common secret key which attains, or gets close to, the information theory bound. Coding theory is then used to ensure that the two communicating parties have a common secret key by using the hash function relating to a code C. The chapter also discusses the extensions of a binary symmetric channel and provides some additional discussion on entropy. It shows how a Shannon function H(p,q) can be expanded in infinitely many ways in an infinite series of functions each of which is a linear combination of Shannon functions of the type H.