A Non-differential Distributed Space-Time Coding for Partially-Coherent Cooperative Communication

In a distributed space-time coding scheme, based on the relay channel model, the relay nodes co-operate to linearly process the transmitted signal from the source and forward them to the destination such that the signal at the destination appears as a space time block code. Recently, a code design criteria for achieving full diversity in a partially-coherent environment have been proposed along with codes based on differential encoding and decoding techniques. For such a set up, in this paper, a non-differential encoding technique and construction of distributed space time block codes from unitary matrix groups at the source and a set of diagonal unitary matrices for the relays are proposed. It is shown that, the performance of our scheme is independent of the choice of unitary matrices at the relays. When the group is cyclic, a necessary and sufficient condition on the generator of the cyclic group to achieve full diversity and to minimize the pairwise error probability is proved. Various choices on the generator of cyclic group to reduce the ML decoding complexity at the destination is presented. It is also shown that, at the source, if non-cyclic abelian unitary matrix groups are used, then full-diversity can not be obtained. The presented scheme is also robust to failure of any subset of relay nodes.Comment: To appear in IEEE Transactions on Wireless Communications. 06 pages, 04 figure

MMSE Optimal Algebraic Space-Time Codes

Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.Comment: 5 pages, 1 figure, journal version to appear in IEEE Transactions on Wireless Communications. Conference version appeared in NCC 2007, IIT Kanpur, Indi

VLSI Implementation of Block Error Correction Coding Techniques

Communication Engineering has become the most vital field of Engineering in today’s life. The world is dreaded to think beyond any communication gadgets. Data communication basically involves transfers of data from one place to another or from one point of time to another. Error may be introduced by the channel which makes data unreliable for user. Hence we need different error detection and error correction schemes. In the present work, we perform the comparative study between different FECs like Turbo codes, Reed-Solomon codes and LPDC codes. But among all these we find Reed Solomon to be most efficient for data communication because of low coding complexity and high coding rate. The RS codes are non-binary, linear and cyclic codes used for burst error correction. They are used in numerous applications like CDs, DVDs and deep space communication. We simulate RS Encoder and RS Decoder for double error correcting RS (7, 3) code. Then we implement RS (255,239) code in VHDL. In RS (255,239) code, each data symbol consists of 8 bits which is quite practical as most of the data transfer is done in terms of bytes. The implementation has been done in the most efficient algorithms to optimize the design in terms of space utilization and latency of the code. The behavioral simulation has been carried out for each block and for the whole design also. Finally, the FPGA utilization and clock cycles needed are analyzed and compared with the already developed designs

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

Perfect Space–Time Block Codes

In this paper, we introduce the notion of perfect space–time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas

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

Space time coding in MIMO systems

Multiple-input multiple-output (MIMO) antenna technology is promising for high-speed wireless communications without increasing the transmission band- width. Space time coding (STC) is a scheme that employs multiple antennas to increase transmission rate or to improve transmission quality. STC is used widely in mobile cellular networks, wireless local area networks (WLAN) and wireless metropolitan area networks (WMAN). However, there are still many unsolved or partially solved issues in STC. In this thesis, I propose a new STC design from cyclic design. I then propose a systematic method to design quasi-orthogonal space time block codes (QOSTBC) for an arbitrary number of transmit antennas, and derive the optimal constellation rotation angles to achieve full diversity. I also propose an analytical method to derive the exact error probabilities of orthogonal space time block codes (OSTBC). In order to improve the error performance, I introduce an adaptive power allocation scheme for OSTBC. Combining STC with continuous phase modulation (CPM) is an attractive solution for mobile commu- nications for which power is limited. Thus, I apply OSTBC to binary CPM with modulation index h = 0.5, and develop a simplified receiver for such scheme. Finally, I present a decoding method to reduce the complexity of QOSTBC without degrading its error performance

On the design of a wireless multi-antenna monitoring system

In this paper we investigate the design of a wireless monitoring system. This system consists of several wireless monitoring units, each transmitting data collected from sensors. This data is received and processed at a central control unit. The typical operating environment poses several challenges. The channel’s delay spread is substantial and the distance between receiver and transmitter is in the order of 400 meters. In order to guarantee reliable communication, we combine multi-antenna techniques (spacetime block coding) with strong coding (LDPC codes). The cost and complexity of the monitoring units is kept low, and most of the processing is performed on the central control unit. We present a system design for the monitoring units and show simulation results

Algebraic Cayley Differential Space–Time 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