We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers. Our technique involves a careful study of a Sato-like upper bound via the solution of a certain algebraic Riccati equation.

In this paper, we introduce the notion of perfect space-time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas

Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to be replenished. Such overheads arise from the fundamental need to recreate (or keep separately) first a copy of the whole object before any individual encoded fragment can be generated and replenished. There has recently been intense interest to explore alternatives, most prominent ones being regenerating codes (RGC) and hierarchical codes (HC). We propose as an alternative a new family of codes to improve the maintenance process, called self-repairing codes (SRC), with the following salient features: (a) encoded fragments can be repaired directly from other subsets of encoded fragments by downloading less data than the size of the complete object, ensuring that (b) a fragment is repaired from a fixed number of encoded fragments, the number depending only on how many encoded blocks are missing and independent of which specific blocks are missing. These properties allow for not only low communication overhead to recreate a missing fragment, but also independent reconstruction of different missing fragments in parallel, possibly in different parts of the network. The fundamental difference between SRCs and HCs is that different encoded fragments in HCs do not have symmetric roles (equal importance). Consequently the number of fragments required to replenish a specific fragment in HCs depends on which specific fragments are missing, and not solely on how many. Likewise, object reconstruction may need different number of fragments depending on which fragments are missing. RGCs apply network coding over (n, k) erasure codes, and provide network information flow based limits on the minimal maintenance overheads. RGCs need to communicate with at least k other nodes to recreate any fragment, and the minimal overhead is achieved if only one fragment is missing, and information is downloaded from all the other n-1 nodes. We analyze the static resilience of SRCs with respect to erasure codes, and observe that SRCs incur marginally larger storage overhead in order to achieve the aforementioned properties. The salient SRC properties naturally translate to low communication overheads for reconstruction of lost fragments, and allow reconstruction with lower latency by facilitating repairs in parallel. These desirable properties make SRC a practical candidate for networked distributed storage systems.

We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers. Our technique involves a careful study of a Sato-like upper bound via the solution of a certain algebraic Riccati equation.

This tutorial reviews fundamental contributions to information security. An integrative viewpoint is taken that explains the security metrics, including secrecy, privacy, and others, the methodology of information-theoretic approaches, along with the arising system design principles, as well as techniques that enable the information-theoretic designs to be applied in real communication and computing systems. The tutorial, while summarizing these contributions, argues for the simultaneous pivotal role of fundamental limits and coding techniques for secure communication system design.

In this correspondence, we present various families of full diversity rotated Z/sup n/-lattice constellations based on algebraic number theory constructions. We are able to give closed-form expressions of their minimum product distance using the corresponding algebraic properties.