Fast-Decodable Asymmetric Space-Time Codes from Division Algebras

Multiple-input double-output (MIDO) codes are important in the near-future wireless communications, where the portable end-user device is physically small and will typically contain at most two receive antennas. Especially tempting is the 4 x 2 channel due to its immediate applicability in the digital video broadcasting (DVB). Such channels optimally employ rate-two space-time (ST) codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general very complex to decode, hence setting forth a call for constructions with reduced complexity. Recently, some reduced complexity constructions have been proposed, but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes. In this paper, it will be shown that a family of division algebra based MIDO codes will always result in at least 37.5% worst-case complexity reduction, while maintaining full diversity and, for the first time, the non-vanishing determinant (NVD) property. The reduction follows from the fact that, similarly to the Alamouti code, the codes will be subsets of matrix rings of the Hamiltonian quaternions, hence allowing simplified decoding. At the moment, such reductions are among the best known for rate-two MIDO codes. Several explicit constructions are presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October 201

Finite automata for testing uniqueness of Eulerian trails

We investigate the condition under which the Eulerian trail of a digraph is unique, and design a finite automaton to examine it. The algorithm is effective, for if the condition is violated, it will be noticed immediately without the need to trace through the whole trail

Prioritized data synchronization with applications

We are interested on the problem of synchronizing data on two distinct devices with differed priorities using minimum communication. A variety of distributed sys- tems require communication efficient and prioritized synchronization, for example, where the bandwidth is limited or certain information is more time sensitive than others. Our particular approach, P-CPI, involving the interactive synchronization of prioritized data, is efficient both in communication and computation. This protocol sports some desirable features, including (i) communication and computational com- plexity primarily tied to the number of di erences between the hosts rather than the amount of the data overall and (ii) a memoryless fast restart after interruption. We provide a novel analysis of this protocol, with proved high-probability performance bound and fast-restart in logarithmic time. We also provide an empirical model for predicting the probability of complete synchronization as a function of time and symmetric differences. We then consider two applications of our core algorithm. The first is a string reconciliation protocol, for which we propose a novel algorithm with online time com- plexity that is linear in the size of the string. Our experimental results show that our string reconciliation protocol can potentially outperform existing synchroniza- tion tools such like rsync in some cases. We also look into the benefit brought by our algorithm to delay-tolerant networks(DTNs). We propose an optimized DTN routing protocol with P-CPI implemented as middleware. As a proof of concept, we demonstrate improved delivery rate, reduced metadata and reduced average delay

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