Rényi Bounds on Information Combining
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Rényi Bounds on Information Combining. / Hirche, Christoph.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. IEEE, 2020. p. 2297-2302 9174256.Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Rényi Bounds on Information Combining
AU - Hirche, Christoph
PY - 2020
Y1 - 2020
N2 - Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in information theory, particularly in coding and Shannon theory. The arguably most elementary kind of information combining is the addition of two binary random variables, i.e. a CNOT gate, and the resulting quantities are fundamental when investigating belief propagation and polar coding.In this work we will generalize the concept to Rényi entropies. We give optimal bounds on the conditional Rényi entropy after combination, based on a certain convexity or concavity property and discuss when this property indeed holds. Since there is no generally agreed upon definition of the conditional Rényi entropy, we consider four different versions from the literature.Finally, we discuss the application of these bounds to the polarization of Rényi entropies under polar codes.
AB - Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in information theory, particularly in coding and Shannon theory. The arguably most elementary kind of information combining is the addition of two binary random variables, i.e. a CNOT gate, and the resulting quantities are fundamental when investigating belief propagation and polar coding.In this work we will generalize the concept to Rényi entropies. We give optimal bounds on the conditional Rényi entropy after combination, based on a certain convexity or concavity property and discuss when this property indeed holds. Since there is no generally agreed upon definition of the conditional Rényi entropy, we consider four different versions from the literature.Finally, we discuss the application of these bounds to the polarization of Rényi entropies under polar codes.
U2 - 10.1109/ISIT44484.2020.9174256
DO - 10.1109/ISIT44484.2020.9174256
M3 - Article in proceedings
AN - SCOPUS:85090404332
SP - 2297
EP - 2302
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PB - IEEE
T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020
Y2 - 21 July 2020 through 26 July 2020
ER -
ID: 256725137