73,907 research outputs found
Weak Secrecy in the Multi-Way Untrusted Relay Channel with Compute-and-Forward
We investigate the problem of secure communications in a Gaussian multi-way
relay channel applying the compute-and-forward scheme using nested lattice
codes. All nodes employ half-duplex operation and can exchange confidential
messages only via an untrusted relay. The relay is assumed to be honest but
curious, i.e., an eavesdropper that conforms to the system rules and applies
the intended relaying scheme. We start with the general case of the
single-input multiple-output (SIMO) L-user multi-way relay channel and provide
an achievable secrecy rate region under a weak secrecy criterion. We show that
the securely achievable sum rate is equivalent to the difference between the
computation rate and the multiple access channel (MAC) capacity. Particularly,
we show that all nodes must encode their messages such that the common
computation rate tuple falls outside the MAC capacity region of the relay. We
provide results for the single-input single-output (SISO) and the
multiple-input single-input (MISO) L-user multi-way relay channel as well as
the two-way relay channel. We discuss these results and show the dependency
between channel realization and achievable secrecy rate. We further compare our
result to available results in the literature for different schemes and show
that the proposed scheme operates close to the compute-and-forward rate without
secrecy.Comment: submitted to JSAC Special Issue on Fundamental Approaches to Network
Coding in Wireless Communication System
Relative Generalized Rank Weight of Linear Codes and Its Applications to Network Coding
By extending the notion of minimum rank distance, this paper introduces two
new relative code parameters of a linear code C_1 of length n over a field
extension and its subcode C_2. One is called the relative
dimension/intersection profile (RDIP), and the other is called the relative
generalized rank weight (RGRW). We clarify their basic properties and the
relation between the RGRW and the minimum rank distance. As applications of the
RDIP and the RGRW, the security performance and the error correction capability
of secure network coding, guaranteed independently of the underlying network
code, are analyzed and clarified. We propose a construction of secure network
coding scheme, and analyze its security performance and error correction
capability as an example of applications of the RDIP and the RGRW. Silva and
Kschischang showed the existence of a secure network coding in which no part of
the secret message is revealed to the adversary even if any dim C_1-1 links are
wiretapped, which is guaranteed over any underlying network code. However, the
explicit construction of such a scheme remained an open problem. Our new
construction is just one instance of secure network coding that solves this
open problem.Comment: IEEEtran.cls, 25 pages, no figure, accepted for publication in IEEE
Transactions on Information Theor
Universal Secure Multiplex Network Coding with Dependent and Non-Uniform Messages
We consider the random linear precoder at the source node as a secure network
coding. We prove that it is strongly secure in the sense of Harada and Yamamoto
and universal secure in the sense of Silva and Kschischang, while allowing
arbitrary small but nonzero mutual information to the eavesdropper. Our
security proof allows statistically dependent and non-uniform multiple secret
messages, while all previous constructions of weakly or strongly secure network
coding assumed independent and uniform messages, which are difficult to be
ensured in practice.Comment: 10 pages, 1 figure, IEEEtrans.cls. Online published in IEEE Trans.
Inform. Theor
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