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Spacetime codes for high data rate wireless communication: Performance criterion and code construction
 IEEE Trans. Inform. Theory
, 1998
"... Abstract — We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into � streams that are simultaneously transmitted using � tr ..."
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Cited by 1225 (25 self)
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Abstract — We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into � streams that are simultaneously transmitted using � transmit antennas. The received signal at each receive antenna is a linear superposition of the � transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2–3 dB of the outage capacity for these channels using only 64 state encoders.
Fading Channels: InformationTheoretic And Communications Aspects
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... In this paper we review the most peculiar and interesting informationtheoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information ..."
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Cited by 289 (1 self)
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In this paper we review the most peculiar and interesting informationtheoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both singleuser and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.
Multilevel Codes: Theoretical Concepts and Practical Design Rules
, 1999
"... This paper deals with 2 ` ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a ..."
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Cited by 128 (24 self)
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This paper deals with 2 ` ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a large space of rate combinations such that MLC and full maximumlikelihood decoding (MLD) can approach capacity. It is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of MLD. The capacity rule, the balanced distances rules, and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design. Simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies. Moreover, topics relevant in practical applications such as signal set labeling, dimensional...
A ratesplitting approach to the Gaussian multipleaccess channel
 IEEE TRANS. INFORM. THEORY
, 1996
"... It is shown that any point in the capacity region of a Gaussian multipleaccess channel is achievable by singleuser coding without requiring synchronization among users, provided that each user “splits” data and signal into two parts. Based on this result, a new multipleaccess technique called rat ..."
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Cited by 81 (2 self)
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It is shown that any point in the capacity region of a Gaussian multipleaccess channel is achievable by singleuser coding without requiring synchronization among users, provided that each user “splits” data and signal into two parts. Based on this result, a new multipleaccess technique called ratesplitting multiple accessing (RSMA) is proposed. RSMA is a codedivision multipleaccess scheme for the Muser Gaussian multipleaccess channel for which the effort of finding the codes for the M users, of encoding, and of decoding is that of at most 2M  1 independent pointtopoint Gaussian channels. The effects of bursty sources, multipath fading, and intercell interference are discussed and directions for further research are indicated.
Distributed source coding: Symmetric rates and applications to sensor networks.
 PROCEEDINGS OF THE DATA COMPRESSION CONFERENCE (DCC
, 2000
"... We address the problem of distributed source coding using a practical and constructive approach [1], referred to as Distributed source coding using syndromes (DISCUS), with applications to sensor networks. We propose low complexity encoding and decoding methods based on linear codes, to achieve all ..."
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Cited by 70 (3 self)
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We address the problem of distributed source coding using a practical and constructive approach [1], referred to as Distributed source coding using syndromes (DISCUS), with applications to sensor networks. We propose low complexity encoding and decoding methods based on linear codes, to achieve all points in the achievable rate region of SlepianWolf [2] problem. The extension of these concepts to the construction of Euclideanspace codes is also studied and analyzed for the case of trellis and lattice codes. The performance of these symmetric methods for encoding with a fidelity criterion is shown to be the same as that of asymmetric encoding. Simulations are presented to corroborate these results.
Optimal tight frames and quantum measurement
 IEEE Trans. Inform. Theory
, 2002
"... Tight frames and rankone quantum measurements are shown to be intimately related. In fact, the family of normalized tight frames for the space in which a quantum mechanical system lies is precisely the family of rankone generalized quantum measurements (POVMs) on that space. Using this relationshi ..."
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Cited by 41 (10 self)
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Tight frames and rankone quantum measurements are shown to be intimately related. In fact, the family of normalized tight frames for the space in which a quantum mechanical system lies is precisely the family of rankone generalized quantum measurements (POVMs) on that space. Using this relationship, frametheoretical analogues of various quantummechanical concepts and results are developed. The analogue of a leastsquares quantum measurement is a tight frame that is closest in a leastsquares sense to a given set of vectors. The leastsquares tight frame is found for both the case in which the scaling of the frame is specified (constrained leastsquares frame (CLSF)) and the case in which the scaling is free (unconstrained leastsquares frame (ULSF)). The wellknown canonical frame is shown to be proportional to the ULSF and to coincide with the CLSF with a certain scaling. Finally, the canonical frame vectors corresponding to a geometrically uniform vector set are shown to be geometrically uniform and to have the same symmetries as the original vector set.
Geometrically uniform frames
 IEEE Trans. Inform. Theory
, 2003
"... Abstract—We introduce a new class of finitedimensional frames with strong symmetry properties, called geometrically uniform (GU) frames, that are defined over a finite Abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to comp ..."
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Cited by 37 (12 self)
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Abstract—We introduce a new class of finitedimensional frames with strong symmetry properties, called geometrically uniform (GU) frames, that are defined over a finite Abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to compound GU (CGU) frames which are generated by a finite Abelian group of unitary matrices using multiple generating vectors. The dual frame vectors and canonical tight frame vectors associated with GU frames are shown to be GU and, therefore, also generated by a single generating vector, which can be computed very efficiently using a Fourier transform (FT) defined over the generating group of the frame. Similarly, the dual frame vectors and canonical tight frame vectors associated with CGU frames are shown to be CGU. The impact of removing single or multiple elements from a GU frame is considered. A systematic method for constructing optimal GU frames from a given set of frame vectors that are not GU is also developed. Finally, the Euclidean distance properties of GU frames are discussed and conditions are derived on the Abelian group of unitary matrices to yield GU frames with strictly positive distance spectrum irrespective of the generating vector. Index Terms—Compound geometrically uniform (CGU) frames, generalized Fourier transform (FT), geometrically uniform (GU) frames, least squares. I.
On quantum detection and the squareroot measurement
 IEEE TRANS. INFORM. THEORY
, 2001
"... In this paper, we consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states. We consider a collection of pure states and seek a positive operatorvalued measure (POVM) consisting of rankone operators with measurement ve ..."
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Cited by 36 (16 self)
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In this paper, we consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states. We consider a collection of pure states and seek a positive operatorvalued measure (POVM) consisting of rankone operators with measurement vectors closest in squared norm to the given states. We compare our results to previous measurements suggested by Peres and Wootters [11] and Hausladen et al. [10], where we refer to the latter as the squareroot measurement (SRM). We obtain a new characterization of the SRM, and prove that it is optimal in a leastsquares sense. In addition, we show that for a geometrically uniform state set the SRM minimizes the probability of a detection error. This generalizes a similar result of Ban et al. [7].
Further Results on SpaceTime Coding for Rayleigh Fading
, 1998
"... transmitter diversity I just need to put these keywords into a coherent statement spacetime codes geometric uniformity uniform distance spectrum code design design metrics effective product distance effective Hamming distance rank and determinant criteria delay diversity I. INTRODUCTION Trellis c ..."
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Cited by 33 (6 self)
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transmitter diversity I just need to put these keywords into a coherent statement spacetime codes geometric uniformity uniform distance spectrum code design design metrics effective product distance effective Hamming distance rank and determinant criteria delay diversity I. INTRODUCTION Trellis coded modulation (TCM) was introduced by Ungerboeck [1] as a form of low complexity, bandwidth efficient coding for AWGN channels. The performance of TCM on fading channels was first analyzed by Divsalar and Simon [2], and using the Chernoff bound they proved that for fading channels it is more important to optimize the Hamming and product distances than Euclidean distance. Numerous researchers have designed many trellis codes for independently fading channels [3]. Traditional code design for fading channels assumes interleaving can make the fading independent. However, if the mobile unit is not moving, infinite interleaving depth would be required. Transmitter diversity [4], [7], [5] can be ...
The NordstromRobinson code is the binary image of the octacode
 Proceedings DIMACS/IEEE Workshop on Coding and
, 1992
"... The NordstromRobinson code, a nonlinear binary code of length 16 and minimal Hamming distance 6, is the binary image of the octacode, a linear selfdual code over 4 of length 8 and minimal Lee distance 6. Since the octacode is the 4analogue of a Hamming code, this ..."
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Cited by 23 (10 self)
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The NordstromRobinson code, a nonlinear binary code of length 16 and minimal Hamming distance 6, is the binary image of the octacode, a linear selfdual code over 4 of length 8 and minimal Lee distance 6. Since the octacode is the 4analogue of a Hamming code, this