1,352 research outputs found
Cyclic division algebras: a tool for space-time coding
Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank.
Extensive work has been done on Space–Time coding, aiming at
finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to
improve the design of good codes.
The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes
Efficient Integer Coefficient Search for Compute-and-Forward
Integer coefficient selection is an important decoding step in the
implementation of compute-and-forward (C-F) relaying scheme. Choosing the
optimal integer coefficients in C-F has been shown to be a shortest vector
problem (SVP) which is known to be NP hard in its general form. Exhaustive
search of the integer coefficients is only feasible in complexity for small
number of users while approximation algorithms such as Lenstra-Lenstra-Lovasz
(LLL) lattice reduction algorithm only find a vector within an exponential
factor of the shortest vector. An optimal deterministic algorithm was proposed
for C-F by Sahraei and Gastpar specifically for the real valued channel case.
In this paper, we adapt their idea to the complex valued channel and propose an
efficient search algorithm to find the optimal integer coefficient vectors over
the ring of Gaussian integers and the ring of Eisenstein integers. A second
algorithm is then proposed that generalises our search algorithm to the
Integer-Forcing MIMO C-F receiver. Performance and efficiency of the proposed
algorithms are evaluated through simulations and theoretical analysis.Comment: IEEE Transactions on Wireless Communications, to appear.12 pages, 8
figure
Algebraic Approach to Physical-Layer Network Coding
The problem of designing physical-layer network coding (PNC) schemes via
nested lattices is considered. Building on the compute-and-forward (C&F)
relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain
using information-theoretic tools, an algebraic approach is taken to show its
potential in practical, non-asymptotic, settings. A general framework is
developed for studying nested-lattice-based PNC schemes---called lattice
network coding (LNC) schemes for short---by making a direct connection between
C&F and module theory. In particular, a generic LNC scheme is presented that
makes no assumptions on the underlying nested lattice code. C&F is
re-interpreted in this framework, and several generalized constructions of LNC
schemes are given. The generic LNC scheme naturally leads to a linear network
coding channel over modules, based on which non-coherent network coding can be
achieved. Next, performance/complexity tradeoffs of LNC schemes are studied,
with a particular focus on hypercube-shaped LNC schemes. The error probability
of this class of LNC schemes is largely determined by the minimum inter-coset
distances of the underlying nested lattice code. Several illustrative
hypercube-shaped LNC schemes are designed based on Construction A and D,
showing that nominal coding gains of 3 to 7.5 dB can be obtained with
reasonable decoding complexity. Finally, the possibility of decoding multiple
linear combinations is considered and related to the shortest independent
vectors problem. A notion of dominant solutions is developed together with a
suitable lattice-reduction-based algorithm.Comment: Submitted to IEEE Transactions on Information Theory, July 21, 2011.
Revised version submitted Sept. 17, 2012. Final version submitted July 3,
201
Distributed Space Time Coding for Wireless Two-way Relaying
We consider the wireless two-way relay channel, in which two-way data
transfer takes place between the end nodes with the help of a relay. For the
Denoise-And-Forward (DNF) protocol, it was shown by Koike-Akino et. al. that
adaptively changing the network coding map used at the relay greatly reduces
the impact of Multiple Access interference at the relay. The harmful effect of
the deep channel fade conditions can be effectively mitigated by proper choice
of these network coding maps at the relay. Alternatively, in this paper we
propose a Distributed Space Time Coding (DSTC) scheme, which effectively
removes most of the deep fade channel conditions at the transmitting nodes
itself without any CSIT and without any need to adaptively change the network
coding map used at the relay. It is shown that the deep fades occur when the
channel fade coefficient vector falls in a finite number of vector subspaces of
, which are referred to as the singular fade subspaces. DSTC
design criterion referred to as the \textit{singularity minimization criterion}
under which the number of such vector subspaces are minimized is obtained.
Also, a criterion to maximize the coding gain of the DSTC is obtained. Explicit
low decoding complexity DSTC designs which satisfy the singularity minimization
criterion and maximize the coding gain for QAM and PSK signal sets are
provided. Simulation results show that at high Signal to Noise Ratio, the DSTC
scheme provides large gains when compared to the conventional Exclusive OR
network code and performs slightly better than the adaptive network coding
scheme proposed by Koike-Akino et. al.Comment: 27 pages, 4 figures, A mistake in the proof of Proposition 3 given in
Appendix B correcte
A Like ELGAMAL Cryptosystem But Resistant To Post-Quantum Attacks
The Modulo 1 Factoring Problem (M1FP) is an elegant mathematical problem which could be exploited to design safe cryptographic protocols and encryption schemes that resist to post quantum attacks. The ELGAMAL encryption scheme is a well-known and efficient public key algorithm designed by Taher ELGAMAL from discrete logarithm problem. It is always highly used in Internet security and many other applications after a large number of years. However, the imminent arrival of quantum computing threatens the security of ELGAMAL cryptosystem and impose to cryptologists to prepare a resilient algorithm to quantum computer-based attacks. In this paper we will present a like-ELGAMAL cryptosystem based on the M1FP NP-hard problem. This encryption scheme is very simple but efficient and supposed to be resistant to post quantum attacks
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