471 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
Self-repairing Homomorphic Codes for Distributed Storage Systems
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 been
recently 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, which we
call self-repairing codes (SRC), with the following salient features: (a)
encoded fragments can be repaired directly from other subsets of encoded
fragments without having to reconstruct first the original data, 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. We analyze the static resilience of SRCs with
respect to traditional 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
self-repairing codes a good and practical candidate for networked distributed
storage systems
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
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
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