title: A dynamical systems proof of Kraft-McMillan inequality and its converse for prefix-free codes.
abstract: Uniquely decodable codes are central to lossless data compression in both classical and quantum communication systems. The Kraft-McMillan inequality is a basic result in information theory which gives a necessary and sufficient condition for a code to be uniquely decodable and also has a quantum analogue. In this letter, we provide a novel dynamical systems proof of this inequality and its converse for prefix-free codes (no codeword is a prefix of another-the popular Huffman codes are an example). For constrained sources, the problem is still open.
authors.affiliation: Department of Electronics and Communications Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Kerala, India. nithin@amritapuri.amrita.edu
authors.forename: Nithin
authors.initials: N
authors.lastname: Nagaraj