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MIMO Multiple Access Channel with an Arbitrarily Varying Eavesdropper: Secrecy degrees of freedom
 IEEE TRANSACTIONS ON INFORMATION THEORY, FEBRUARY
, 2013
"... A twotransmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known t ..."
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Cited by 13 (5 self)
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A twotransmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver, and uses a singleuser wiretap code for each user, is shown to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weightedsumrate expression. This is accomplished by using induction, where at each step one combines the secrecy and multipleaccess constraints associated with an adversary eavesdropping a carefully selected group of subchannels.
MIMO Broadcast Channel with Arbitrarily Varying Eavesdropper Channel: Secrecy Degrees of Freedom
 IN IEEE GLOBAL TELECOMMUNICATION CONFERENCE
, 2011
"... A tworeceiver MIMO broadcastwiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper exp ..."
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Cited by 8 (6 self)
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A tworeceiver MIMO broadcastwiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper experiences no additive noise. The channel between the transmitter and the two legitimate receivers is a constant MIMO Gaussian broadcast channel. This paper establishes the secrecy degrees of freedom region for transmitting a commonconfidential message as well as a privateconfidential message to each receiver. It is observed that a straightforward extension of single user random binning does not achieve the optimal secrecy degrees of freedom (s.d.o.f.) region. The proposed coding scheme that achieves the s.d.o.f. region involves simultaneous diagonalization of the channel matrices of the two legitimate receivers using the generalized singular value decomposition (GSVD) as well as a particular structured binning across codebooks that minimizes the rate of the fictitious message. While the focus is on achieving weak secrecy for ease of exposition, an outline is provided on how the results can be extended for achieving strong secrecy.
MIMO Broadcast Channel with an Unknown Eavesdropper: Secrecy Degrees of Freedom
"... Abstract—We study a multiantenna broadcast channel with two legitimate receivers and an external eavesdropper. We assume that the channel matrix of the eavesdropper is unknown to the legitimate terminals but satisfies a maximum rank constraint. As our main result we characterize the associated secr ..."
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Abstract—We study a multiantenna broadcast channel with two legitimate receivers and an external eavesdropper. We assume that the channel matrix of the eavesdropper is unknown to the legitimate terminals but satisfies a maximum rank constraint. As our main result we characterize the associated secrecy degrees of freedom for the broadcast channel with common and private messages. We show that a direct extension of the singleuser wiretap codebook does not achieve the secrecy degrees of freedom. Our proposed optimal scheme involves decomposing the signal space into a common subspace, which can be observed by both receivers, and private subspaces which can be observed by only one of the receivers, and carefully transmitting a subset of messages in each subspace. We also consider the case when each user’s private message must additionally remain confidential from the other legitimate receiver and characterize the s.d.o.f. region in this case. Index Terms—Information theoretic security, broadcast channels, wiretap channels, generalized singular value decomposition, MIMOME channel. I.