Paper 2019/1169

Semantically Secure Lattice Codes for Compound MIMO Channels

Antonio Campello, Cong Ling, and Jean-Claude Belfiore


We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.

Available format(s)
Publication info
Published elsewhere. MINOR revision.IEEE TRANSACTIONS ON INFORMATION THEORY, to be published in 2020
information theorylattices
Contact author(s)
c ling @ imperial ac uk
2019-10-10: received
Short URL
Creative Commons Attribution


      author = {Antonio Campello and Cong Ling and Jean-Claude Belfiore},
      title = {Semantically Secure Lattice Codes for Compound MIMO Channels},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1169},
      year = {2019},
      note = {\url{}},
      url = {}
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