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On the Fundamental Limits of Coded Caching With Correlated Files of Combinatorial Overlaps | IEEE Journals & Magazine | IEEE Xplore

On the Fundamental Limits of Coded Caching With Correlated Files of Combinatorial Overlaps


Abstract:

This paper studies the fundamental limits of the shared-link coded caching problem with correlated files, where a server with a library of {\mathsf N} files communica...Show More

Abstract:

This paper studies the fundamental limits of the shared-link coded caching problem with correlated files, where a server with a library of {\mathsf N} files communicates with {\mathsf K} users who can locally cache {\mathsf M} files. Given an integer {\mathsf r}\in [{\mathsf N}] , correlation is modelled as follows: each {\mathsf r} -subset of files contains a unique common block. The tradeoff between the cache size and the average transmitted load over the uniform demand distribution is studied. First, a converse bound under the constraint of uncoded cache placement (i.e., each user directly stores a subset of the library bits) is derived. Then, a caching scheme for the case where every user demands a distinct file (possible for {\mathsf N}\geq {\mathsf K} ) is shown to be optimal under the constraint of uncoded cache placement. This caching scheme is further proved to be decodable and optimal under the constraint of uncoded cache placement when (i) {\mathsf K} {\mathsf r} {\mathsf M}\leq 2 {\mathsf N} or {\mathsf K} {\mathsf r} {\mathsf M}\geq ({\mathsf K}-1) {\mathsf N} or {\mathsf r}\in \{1,2, {\mathsf N}-1, {\mathsf N}\} , and (ii) when the number of distinct demanded files is no larger than four. Finally, a new delivery scheme based on interference alignment which jointly serves the users’ demands is shown to be order optimal to within a factor of 2 under the constraint of uncoded cache placement. As an extension, the above exact and order optimal results can be extended to the worst-case load. As by-products, an extension of the proposed scheme for {\mathsf M}= {\mathsf N}/ {\mathsf K} is shown to reduce the load of state-of-the-art schemes for the coded caching problem where the users can request multiple files; the proposed scheme for distinct demands can be extended to the coded distributed computing problem with a central server, which achieves the optimal transmission load over the binary field.
Published in: IEEE Transactions on Information Theory ( Volume: 69, Issue: 10, October 2023)
Page(s): 6376 - 6400
Date of Publication: 30 June 2023

ISSN Information:

Funding Agency:

Electrical Engineering and Computer Science Department, Technische Universität Berlin, Berlin, Germany
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, China
Kai Wan (Member, IEEE) received the B.E. degree in optoelectronics from the Huazhong University of Science and Technology, China, in 2012, and the M.Sc. and Ph.D. degrees in communications from Université Paris-Saclay, France, in 2014 and 2018, respectively. Subsequently, he was a Post-Doctoral Researcher with the Communications and Information Theory Chair (CommIT), Technische Universität Berlin, Berlin, Germany. He is c...Show More
Kai Wan (Member, IEEE) received the B.E. degree in optoelectronics from the Huazhong University of Science and Technology, China, in 2012, and the M.Sc. and Ph.D. degrees in communications from Université Paris-Saclay, France, in 2014 and 2018, respectively. Subsequently, he was a Post-Doctoral Researcher with the Communications and Information Theory Chair (CommIT), Technische Universität Berlin, Berlin, Germany. He is c...View more
Electrical and Computer Engineering Department, University of Illinois Chicago, Chicago, IL, USA
Daniela Tuninetti (Fellow, IEEE) received the Ph.D. degree in electrical engineering from ENST/Télécom ParisTech, Paris, France, in 2002 (with work done at the Eurecom Institute in Sophia Antipolis, France). She is currently a Professor with the Department of Electrical and Computer Engineering, University of Illinois Chicago (UIC), where she joined in 2005. She was a Post-Doctoral Research Associate with the School of Co...Show More
Daniela Tuninetti (Fellow, IEEE) received the Ph.D. degree in electrical engineering from ENST/Télécom ParisTech, Paris, France, in 2002 (with work done at the Eurecom Institute in Sophia Antipolis, France). She is currently a Professor with the Department of Electrical and Computer Engineering, University of Illinois Chicago (UIC), where she joined in 2005. She was a Post-Doctoral Research Associate with the School of Co...View more
Electrical and Computer Engineering Department, The University of Utah, Salt Lake City, UT, USA
Mingyue Ji (Member, IEEE) received the B.E. degree in communication engineering from the Beijing University of Posts and Telecommunications, China, in 2006, the M.Sc. degrees in electrical engineering from the Royal Institute of Technology, Sweden, and the University of California, Santa Cruz, in 2008 and 2010, respectively, and the Ph.D. degree from the Ming Hsieh Department of Electrical Engineering, University of South...Show More
Mingyue Ji (Member, IEEE) received the B.E. degree in communication engineering from the Beijing University of Posts and Telecommunications, China, in 2006, the M.Sc. degrees in electrical engineering from the Royal Institute of Technology, Sweden, and the University of California, Santa Cruz, in 2008 and 2010, respectively, and the Ph.D. degree from the Ming Hsieh Department of Electrical Engineering, University of South...View more
Electrical Engineering and Computer Science Department, Technische Universität Berlin, Berlin, Germany
Giuseppe Caire (Fellow, IEEE) was born in Torino in 1965. He received the B.Sc. degree in electrical engineering from Politecnico di Torino in 1990, the M.Sc. degree in electrical engineering from Princeton University in 1992, and the Ph.D. degree from Politecnico di Torino in 1994. He was a Post-Doctoral Research Fellow with the European Space Agency (ESTEC), Noordwijk, The Netherlands, from 1994 to 1995; an Assistant Pr...Show More
Giuseppe Caire (Fellow, IEEE) was born in Torino in 1965. He received the B.Sc. degree in electrical engineering from Politecnico di Torino in 1990, the M.Sc. degree in electrical engineering from Princeton University in 1992, and the Ph.D. degree from Politecnico di Torino in 1994. He was a Post-Doctoral Research Fellow with the European Space Agency (ESTEC), Noordwijk, The Netherlands, from 1994 to 1995; an Assistant Pr...View more

Electrical Engineering and Computer Science Department, Technische Universität Berlin, Berlin, Germany
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, China
Kai Wan (Member, IEEE) received the B.E. degree in optoelectronics from the Huazhong University of Science and Technology, China, in 2012, and the M.Sc. and Ph.D. degrees in communications from Université Paris-Saclay, France, in 2014 and 2018, respectively. Subsequently, he was a Post-Doctoral Researcher with the Communications and Information Theory Chair (CommIT), Technische Universität Berlin, Berlin, Germany. He is currently a Professor with the School of Electronic Information and Communications, Huazhong University of Science and Technology. His research interests include information theory, coding techniques and their applications on coded caching, index coding, distributed storage, distributed computing, wireless communications, and privacy and security. He has served as an Associate Editor for IEEE Communications Letters in August 2021.
Kai Wan (Member, IEEE) received the B.E. degree in optoelectronics from the Huazhong University of Science and Technology, China, in 2012, and the M.Sc. and Ph.D. degrees in communications from Université Paris-Saclay, France, in 2014 and 2018, respectively. Subsequently, he was a Post-Doctoral Researcher with the Communications and Information Theory Chair (CommIT), Technische Universität Berlin, Berlin, Germany. He is currently a Professor with the School of Electronic Information and Communications, Huazhong University of Science and Technology. His research interests include information theory, coding techniques and their applications on coded caching, index coding, distributed storage, distributed computing, wireless communications, and privacy and security. He has served as an Associate Editor for IEEE Communications Letters in August 2021.View more
Electrical and Computer Engineering Department, University of Illinois Chicago, Chicago, IL, USA
Daniela Tuninetti (Fellow, IEEE) received the Ph.D. degree in electrical engineering from ENST/Télécom ParisTech, Paris, France, in 2002 (with work done at the Eurecom Institute in Sophia Antipolis, France). She is currently a Professor with the Department of Electrical and Computer Engineering, University of Illinois Chicago (UIC), where she joined in 2005. She was a Post-Doctoral Research Associate with the School of Communication and Computer Science, Swiss Federal Institute of Technology in Lausanne (EPFL), Lausanne, Switzerland, from 2002 to 2004. Her research interests include ultimate performance limits of wireless interference networks (with a special emphasis on cognition and user cooperation), coexistence between radar and communication systems, multi-relay networks, content-type coding, cache-aided systems, and distributed private coded computing. She was a recipient of the Best Paper Award at the European Wireless Conference in 2002, the NSF CAREER Award in 2007, and named University of Illinois Scholar in 2015. She was the Editor-in-Chief of the IEEE Information Theory Society Newsletter, from 2006 to 2008; and an Editor of IEEE Communication Letters, from 2006 to 2009, IEEE Transactions on Wireless Communications, from 2011 to 2014, and IEEE Transactions on Information Theory, from 2014 to 2017. She is also currently an Editor of IEEE Transactions on Communications. She is currently a Distinguished Lecturer of the Information Theory Society.
Daniela Tuninetti (Fellow, IEEE) received the Ph.D. degree in electrical engineering from ENST/Télécom ParisTech, Paris, France, in 2002 (with work done at the Eurecom Institute in Sophia Antipolis, France). She is currently a Professor with the Department of Electrical and Computer Engineering, University of Illinois Chicago (UIC), where she joined in 2005. She was a Post-Doctoral Research Associate with the School of Communication and Computer Science, Swiss Federal Institute of Technology in Lausanne (EPFL), Lausanne, Switzerland, from 2002 to 2004. Her research interests include ultimate performance limits of wireless interference networks (with a special emphasis on cognition and user cooperation), coexistence between radar and communication systems, multi-relay networks, content-type coding, cache-aided systems, and distributed private coded computing. She was a recipient of the Best Paper Award at the European Wireless Conference in 2002, the NSF CAREER Award in 2007, and named University of Illinois Scholar in 2015. She was the Editor-in-Chief of the IEEE Information Theory Society Newsletter, from 2006 to 2008; and an Editor of IEEE Communication Letters, from 2006 to 2009, IEEE Transactions on Wireless Communications, from 2011 to 2014, and IEEE Transactions on Information Theory, from 2014 to 2017. She is also currently an Editor of IEEE Transactions on Communications. She is currently a Distinguished Lecturer of the Information Theory Society.View more
Electrical and Computer Engineering Department, The University of Utah, Salt Lake City, UT, USA
Mingyue Ji (Member, IEEE) received the B.E. degree in communication engineering from the Beijing University of Posts and Telecommunications, China, in 2006, the M.Sc. degrees in electrical engineering from the Royal Institute of Technology, Sweden, and the University of California, Santa Cruz, in 2008 and 2010, respectively, and the Ph.D. degree from the Ming Hsieh Department of Electrical Engineering, University of Southern California, in 2015. Subsequently, he was a Staff II System Design Scientist with Broadcom Corporation (Broadcom Ltd.), from 2015 to 2016. He is currently an Associate Professor with the Electrical and Computer Engineering Department and an Adjunct Associate Professor with the School of Computing, The University of Utah. His research interests include information theory, coding theory, concentration of measure and statistics, with the applications of distributed computing systems, wireless communications and networking, caching networks, distributed machine learning, distributed storage, and (statistical) signal processing. He has received the NSF CAREER Award in 2022, the IEEE Communications Society Leonard G. Abraham Prize for the Best IEEE Journal on Selected Areas in Communications Paper in 2019, the Best Paper Awards at 2021 IEEE GLOBECOM Conference and 2015 IEEE ICC Conference, the Best Student Paper Award at 2010 IEEE European Wireless Conference, and the USC Annenberg Fellowship from 2010 to 2014. He has been serving as an Associate Editor for IEEE Transactions on Information Theory, since 2022, and IEEE Transactions on Communications, since 2020.
Mingyue Ji (Member, IEEE) received the B.E. degree in communication engineering from the Beijing University of Posts and Telecommunications, China, in 2006, the M.Sc. degrees in electrical engineering from the Royal Institute of Technology, Sweden, and the University of California, Santa Cruz, in 2008 and 2010, respectively, and the Ph.D. degree from the Ming Hsieh Department of Electrical Engineering, University of Southern California, in 2015. Subsequently, he was a Staff II System Design Scientist with Broadcom Corporation (Broadcom Ltd.), from 2015 to 2016. He is currently an Associate Professor with the Electrical and Computer Engineering Department and an Adjunct Associate Professor with the School of Computing, The University of Utah. His research interests include information theory, coding theory, concentration of measure and statistics, with the applications of distributed computing systems, wireless communications and networking, caching networks, distributed machine learning, distributed storage, and (statistical) signal processing. He has received the NSF CAREER Award in 2022, the IEEE Communications Society Leonard G. Abraham Prize for the Best IEEE Journal on Selected Areas in Communications Paper in 2019, the Best Paper Awards at 2021 IEEE GLOBECOM Conference and 2015 IEEE ICC Conference, the Best Student Paper Award at 2010 IEEE European Wireless Conference, and the USC Annenberg Fellowship from 2010 to 2014. He has been serving as an Associate Editor for IEEE Transactions on Information Theory, since 2022, and IEEE Transactions on Communications, since 2020.View more
Electrical Engineering and Computer Science Department, Technische Universität Berlin, Berlin, Germany
Giuseppe Caire (Fellow, IEEE) was born in Torino in 1965. He received the B.Sc. degree in electrical engineering from Politecnico di Torino in 1990, the M.Sc. degree in electrical engineering from Princeton University in 1992, and the Ph.D. degree from Politecnico di Torino in 1994. He was a Post-Doctoral Research Fellow with the European Space Agency (ESTEC), Noordwijk, The Netherlands, from 1994 to 1995; an Assistant Professor of telecommunications with Politecnico di Torino; an Associate Professor with the University of Parma, Italy; a Professor with the Department of Mobile Communications, Eurecom Institute, Sophia-Antipolis, France; and a Professor of electrical engineering with the Viterbi School of Engineering, University of Southern California, Los Angeles. He is currently an Alexander von Humboldt Professor with the Faculty of Electrical Engineering and Computer Science, Technische Universität Berlin, Germany. His main research interests include communications theory, information theory, and channel and source coding, with particular focus on wireless communications. He received the Jack Neubauer Best System Paper Award from the IEEE Vehicular Technology Society in 2003, the IEEE Communications Society and Information Theory Society Joint Paper Award in 2004 and 2011, the Okawa Research Award in 2006, the Alexander von Humboldt Professorship in 2014, the Vodafone Innovation Prize in 2015, an ERC Advanced Grant in 2018, the Leonard G. Abraham Prize for Best IEEE Journal on Selected Areas in Communications Paper in 2019, and the IEEE Communications Society Edwin Howard Armstrong Achievement Award in 2020. He was a recipient of the 2021 Leibinz Prize of the German National Science Foundation (DFG). He has served in the Board of Governors of the IEEE Information Theory Society, from 2004 to 2007, where he was an Officer, from 2008 to 2013. He was a President of the IEEE Information Theory Society in 2011.
Giuseppe Caire (Fellow, IEEE) was born in Torino in 1965. He received the B.Sc. degree in electrical engineering from Politecnico di Torino in 1990, the M.Sc. degree in electrical engineering from Princeton University in 1992, and the Ph.D. degree from Politecnico di Torino in 1994. He was a Post-Doctoral Research Fellow with the European Space Agency (ESTEC), Noordwijk, The Netherlands, from 1994 to 1995; an Assistant Professor of telecommunications with Politecnico di Torino; an Associate Professor with the University of Parma, Italy; a Professor with the Department of Mobile Communications, Eurecom Institute, Sophia-Antipolis, France; and a Professor of electrical engineering with the Viterbi School of Engineering, University of Southern California, Los Angeles. He is currently an Alexander von Humboldt Professor with the Faculty of Electrical Engineering and Computer Science, Technische Universität Berlin, Germany. His main research interests include communications theory, information theory, and channel and source coding, with particular focus on wireless communications. He received the Jack Neubauer Best System Paper Award from the IEEE Vehicular Technology Society in 2003, the IEEE Communications Society and Information Theory Society Joint Paper Award in 2004 and 2011, the Okawa Research Award in 2006, the Alexander von Humboldt Professorship in 2014, the Vodafone Innovation Prize in 2015, an ERC Advanced Grant in 2018, the Leonard G. Abraham Prize for Best IEEE Journal on Selected Areas in Communications Paper in 2019, and the IEEE Communications Society Edwin Howard Armstrong Achievement Award in 2020. He was a recipient of the 2021 Leibinz Prize of the German National Science Foundation (DFG). He has served in the Board of Governors of the IEEE Information Theory Society, from 2004 to 2007, where he was an Officer, from 2008 to 2013. He was a President of the IEEE Information Theory Society in 2011.View more
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