102 research outputs found
On the Optimality of the Golden Code
In this note, we prove the optimality
of the Golden Code inside the class of cyclic algebras
based codes. In doing so, we get better insight on
these algebraic codes, not only in dimension 2, but
more generally for higher dimension, and summarizing
the different approaches tried so far to optimize
them, we derive design strategies that we believe are
the key to either show the optimality of existing codes
or give a way to improve them
Rank weight hierarchy of some classes of cyclic codes
We study the rank weight hierarchy, thus in particular the rank metric, of
cyclic codes over the finite field , a prime power, . We establish the rank weight hierarchy for cyclic codes and
characterize cyclic codes of rank metric 1 when (1) , (2) and
are coprime, and (3) the characteristic divides .
Finally, for and coprime, cyclic codes of minimal -rank are
characterized, and a refinement of the Singleton bound for the rank weight is
derived
The Secrecy Capacity of the MIMO Wiretap Channel
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 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
Code Design for Multihop Wireless Relay Networks
We consider a wireless relay network, where a transmitter node communicates with a receiver node with the help of relay nodes. Most coding strategies considered so far assume that the relay nodes are used for one hop. We address the problem of code design when relay nodes may be used for more than one hop. We consider as a protocol a more elaborated version of amplify-and-forward, called distributed space-time coding, where the relay nodes multiply their received signal with a unitary matrix, in such a way that the receiver senses a space-time code. We first show that in this scenario, as expected, the so-called full-diversity condition holds, namely, the codebook of distributed space-time codewords has to be designed such that the difference of any two distinct codewords is full rank. We then compute the diversity of the channel, and show that it is given by the minimum number of relay nodes among the hops. We finally give a systematic way of building fully diverse codebooks and provide simulation results for their performance
A coding scheme for wireless networks with multiple antenna nodes and no channel information
In this paper, we present a coding strategy for wireless relay networks where the relay nodes are small devices with few resources, while the source and sink are equipped with multiple antennas to increase the transmission rate. We assume no channel knowledge at all, and the receiver decodes knowing none of the channel paths. This coding scheme uses distributed space-time coding techniques and is inspired by noncoherent differential space-time coding. It is shown to yield a diversity linear in the minimum number of transmit/receive antennas times the number of relays
Algebraic Cayley Differential SpaceâTime Codes
Cayley space-time codes have been proposed as a solution for coding over noncoherent differential multiple-input multiple-output (MIMO) channels. Based on the Cayley transform that maps the space of Hermitian matrices to the manifold of unitary matrices, Cayley codes are particularly suitable for high data rate, since they have an easy encoding and can be decoded using a sphere-decoder algorithm. However, at high rate, the problem of evaluating if a Cayley code is fully diverse may become intractable, and previous work has focused instead on maximizing a mutual information criterion. The drawback of this approach is that it requires heavy optimization which depends on the number of antennas and rate. In this work, we study Cayley codes in the context of division algebras, an algebraic tool that allows to get fully diverse codes. We present an algebraic construction of fully diverse Cayley codes, and show that this approach naturally yields, without further optimization, codes that perform similarly or closely to previous unitary differential codes, including previous Cayley codes, and codes built from Lie groups
Cyclic Distributed SpaceâTime Codes for Wireless Relay Networks With No Channel Information
In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver, or relays. The coding scheme uses distributed spaceâtime coding, that is, the relay nodes cooperate to encode the transmitted signal so that the receiver senses a spaceâtime codeword. It is inspired by noncoherent differential techniques. The proposed strategy is available for any number of relays nodes. It is analyzed, and shown to yield a diversity linear in the number of relays. We also study the resistance of the scheme to relay node failures, and show that a network with R relay nodes and d of them down behaves, as far as diversity is concerned, as a network with R-d nodes. Finally, our construction can be easily generalized to the case where the transmitter and receiver nodes have several antennas
An Algebraic Coding Scheme for Wireless Relay Networks With Multiple-Antenna Nodes
We consider the problem of coding over a half-duplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas, whereas each relay is a small device with only a single antenna. Since, in this scenario, requiring the relays to decode results in severe rate hits, we propose a full rate strategy where the relays do a simple operation before forwarding the signal, based on the idea of distributed space-time coding. Our scheme relies on division algebras, an algebraic object which allows the design of fully diverse matrices. The code construction is applicable to systems with any number of transmit/receive antennas and relays, and has better performance than random code constructions, with much less encoding complexity. Finally, the robustness of the proposed distributed space-time codes to node failures is considered
The MIMO wiretap channel
We study the MIMO wiretap channel, 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 ensuring 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
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