<p>Uniquely decodable codes are central to lossless data compression in both classical and quantum communicationsystems. 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.</p>
N. Nagaraj, “A Dynamical Systems Proof of Kraft–McMillan Inequality and its Converse for Prefix-free Codes”, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 19, p. 013136, 2009.