Channel Coding at Low Capacity

Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of mobile networks. Such scenarios require efficient and reliable transmission of information over channels with an extremely small capacity. Within these constraints, the performance of state-of-the-art coding techniques is far from optimal in terms of either rate or complexity. Moreover, the current non-asymptotic laws of optimal channel coding provide inaccurate predictions for coding in the low-capacity regime. In this paper, we provide the first comprehensive study of channel coding in the low-capacity regime. We will investigate the fundamental non-asymptotic limits for channel coding as well as challenges that must be overcome for efficient code design in low-capacity scenarios.Comment: 39 pages, 5 figure

Information-theoretic Physical Layer Security for Satellite Channels

Shannon introduced the classic model of a cryptosystem in 1949, where Eve has access to an identical copy of the cyphertext that Alice sends to Bob. Shannon defined perfect secrecy to be the case when the mutual information between the plaintext and the cyphertext is zero. Perfect secrecy is motivated by error-free transmission and requires that Bob and Alice share a secret key. Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the Shannon model assuming that the channels are noisy and proved that secrecy can be achieved without sharing a secret key. This model is called wiretap channel model and secrecy capacity is known when Eve's channel is noisier than Bob's channel. In this paper we review the concept of wiretap coding from the satellite channel viewpoint. We also review subsequently introduced stronger secrecy levels which can be numerically quantified and are keyless unconditionally secure under certain assumptions. We introduce the general construction of wiretap coding and analyse its applicability for a typical satellite channel. From our analysis we discuss the potential of keyless information theoretic physical layer security for satellite channels based on wiretap coding. We also identify system design implications for enabling simultaneous operation with additional information theoretic security protocols