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54
Achieving nearcapacity on a multipleantenna channel
 IEEE Trans. Commun
, 2003
"... Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve nearcapacity on a singleantenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve nea ..."
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Cited by 233 (2 self)
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Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve nearcapacity on a singleantenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve nearcapacity on a multipleantenna system where the receiver knows the channel. Combining iterative processing with multipleantenna channels is particularly challenging because the channel capacities can be a factor of ten or more higher than their singleantenna counterparts. Using a “list ” version of the sphere decoder, we provide a simple method to iteratively detect and decode any linear spacetime mapping combined with any channel code that can be decoded using socalled “soft ” inputs and outputs. We exemplify our technique by directly transmitting symbols that are coded with a channel code; we show that iterative processing with even this simple scheme can achieve nearcapacity. We consider both simple convolutional and powerful turbo channel codes and show that excellent performance at very high data rates can be attained with either. We compare our simulation results with Shannon capacity limits for ergodic multipleantenna channel. Index Terms—Wireless communications, BLAST, turbo codes, transmit diversity, receive diversity, fading channels, sphere decoding, softin/softout, concatenated codes 1
EXIT charts of irregular codes
, 2002
"... We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregula ..."
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Cited by 54 (7 self)
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We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregular codes can be constructed, which can be used to improve the converence of the iterative decoding algorithm significantly. An efficient and optimal optiamization algorithm is presented. Finally, some results on thresholds on the decoding convergence are outlined.
Optimized Symbol Mappings for BitInterleaved Coded Modulation with Iterative Decoding
 IEEE Commun. Lett
, 2003
"... We investigate bitinterleaved coded modulation with iterative decoding (BICMID) for bandwidth efficient transmission, where the bit error rate is reduced through iterations between a multilevel demapper and a simple channel decoder. In order to achieve a significant turbogain, the assignment stra ..."
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Cited by 50 (10 self)
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We investigate bitinterleaved coded modulation with iterative decoding (BICMID) for bandwidth efficient transmission, where the bit error rate is reduced through iterations between a multilevel demapper and a simple channel decoder. In order to achieve a significant turbogain, the assignment strategy of the binary indices to signal points is crucial. We address the problem of finding the most suitable index assignments to arbitrary, high order signal constellations. A new method based on the binary switching algorithm is proposed that finds optimized mappings outperforming previously known ones.
Design of Serially Concatenated Systems Depending on the Block Length
, 2003
"... We study the convergence behavior of iterative decoding for a number of serially concatenated systems, such as a serially concatenated code, coded data transmission over an intersymbol interference channel, bitinterleaved coded modulation, or trelliscoded modulation. We rederive an existing analy ..."
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Cited by 45 (3 self)
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We study the convergence behavior of iterative decoding for a number of serially concatenated systems, such as a serially concatenated code, coded data transmission over an intersymbol interference channel, bitinterleaved coded modulation, or trelliscoded modulation. We rederive an existing analysis technique called EXIT chart, simplify its construction, and construct simple irregular codes to improve the convergence of iterative decoding. An efficient and optimal optimization algorithm yields systems, which approach information theoretic limits very closely. However, these systems exhibit their performance only for very long block lengths. To overcome this problem, we optimize the decoding convergence after a fixed, finite amount of iterations yielding systems, which perform very well for short block lengths, too. As an example, optimal system configurations for communication over an additive white Gaussian noise channel are presented.
Measures for Tracing Convergence of Iterative Decoding Algorithms
 in Proc. 4th IEEE/ITG Conf. on Source and Channel Coding
, 2002
"... We study the convergence behavior of turbo decoding, turbo equalization, and turbo bitinterleaved coded modulation in a unified framework, which is to regard all three principles as instances of iterative decoding of two serially concatenated codes. There is a collection of measures in the recent l ..."
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Cited by 28 (5 self)
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We study the convergence behavior of turbo decoding, turbo equalization, and turbo bitinterleaved coded modulation in a unified framework, which is to regard all three principles as instances of iterative decoding of two serially concatenated codes. There is a collection of measures in the recent literature, which trace the convergence of iterative decoding algorithms based on a single parameter. This parameter is assumed to completely describe the behavior of the softin softout decoders being part of the iterative algorithm. The measures observe different parameters and were originally applied to different types of decoders. In this paper, we show how six of those measures are related to each other and we compare their convergence prediction capability for the decoding principles mentioned above. We observed that two measures predict the convergence very well for all regarded decoding principles and others suffer from systematic prediction errors independent of the decoding principle.
Convergence Prediction for Iterative Decoding of Threefold Concatenated Systems
 in Proc. IEEE Global Commun. Conf. (GLOBECOM '02
, 2002
"... We show how to use EXIT charts for convergence prediction of a threefold serially concatenated system. The corresponding chart has three dimensions and allows to appropriately select system parameters and to find an optimal schedule of decoding iterations between the three decoders of such a system. ..."
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Cited by 19 (1 self)
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We show how to use EXIT charts for convergence prediction of a threefold serially concatenated system. The corresponding chart has three dimensions and allows to appropriately select system parameters and to find an optimal schedule of decoding iterations between the three decoders of such a system. Convergence thresholds are obtained to determine the minimal signalto noise ratios for which convergence is possible. It turns out that threefold concatenated systems do not achieve any additional performance gain compared to suitably designed twofold systems. We conclude that a threefold concatenation should be considered only when the decoders cannot be chosen freely.
Turbo synchronization: an EM algorithm interpretation
 In Proc. IEEE International Conference on Communications (ICC
, 2003
"... This paper is devoted to turbo synchronization, that is to say the use of soft information to estimate parameters like carrier phase, frequency offset or timing within a turbo receiver. It is shown how maximumlikelihood estimation of those synchronization parameters can be implemented by means of t ..."
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Cited by 18 (5 self)
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This paper is devoted to turbo synchronization, that is to say the use of soft information to estimate parameters like carrier phase, frequency offset or timing within a turbo receiver. It is shown how maximumlikelihood estimation of those synchronization parameters can be implemented by means of the iterative expectationmaximization (EM) algorithm [1]. Then we show that the EM algorithm iterations can be combined with those of a turbo receiver. This leads to a general theoretical framework for turbo synchronization. The soft decisiondirected adhoc algorithm proposed in [2] for carrier phase recovery turns out to be a particular instance of this implementation. The proposed mathematical framework is illustrated by simulations reported for the particular case of carrier phase estimation combined with iterative demodulation and decoding [3].
Constellation labeling for linear encoders
 IEEE TRANS. INFORM. THEORY
, 2001
"... This paper investigates optimal constellation labeling in the context of the edge profile. A constellation’s edge profile lists the minimumdistance edge for each binary symbol error. The paper introduces the symmetricultracomposite (SU) labeling structure and shows that this structure provides un ..."
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Cited by 14 (6 self)
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This paper investigates optimal constellation labeling in the context of the edge profile. A constellation’s edge profile lists the minimumdistance edge for each binary symbol error. The paper introduces the symmetricultracomposite (SU) labeling structure and shows that this structure provides undominated edge profiles for 2PSK, 2PAM, and 22point square QAM. The SU structure is a generalization of the commonly used reflected binary Gray code. With the proper choice of basis vectors, SU labeling can support either setpartition or Graycode labeling of 2PSK, 2PAM, and 22point square QAM. Notably, there are Graycode and setpartition labelings that do not have the SU structure. These labelings yield inferior edge profiles. The SU structure does not apply to cross constellations. However, for any standard cross constellation with 32 or more points, a quasiSU labeling structure can approximate the SU structure. With the correct choice of basis, quasiSU labelings produce quasiGray labelings. However, the quasiSU structure cannot support setpartition labeling. In fact, the quasiSU structure provides a better edge profile than standard setpartition labeling. Thus, for cross constellations there is a choice between edge profile optimality and the group structure provided by setpartitioning. Here, the correct choice depends on whether the encoder trellis has parallel branches.
Low Complexity MMSE Turbo Equalization: A Possible Solution For EDGE
 IEEE TRANS. WIRELESS COMMUN
, 2005
"... This paper deals with a low complexity receiver scheme where equalization and channel decoding are jointly optimized in an iterative process. We derive the theoretical transfer function of the infinite length linear minimum mean square error (MMSE) equalizer with a priori information. A practical im ..."
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Cited by 13 (3 self)
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This paper deals with a low complexity receiver scheme where equalization and channel decoding are jointly optimized in an iterative process. We derive the theoretical transfer function of the infinite length linear minimum mean square error (MMSE) equalizer with a priori information. A practical implementation is exposed which employs the Fast Fourier Transform (FFT) to compute the equalizer tap coefficients, resulting in a low complexity receiver structure. The performance of the proposed scheme is investigated for the Enhanced General Packet Radio Service (EGPRS) radio link. Simulation results show that significant power gains may be achieved with only a few (34) iterations. These results demonstrate that MMSE turbo equalization constitutes an attractive candidate for singlecarrier broadband wireless transmissions in long delayspread environments.
The CramerRao Bound for Phase Estimation From Coded Linearly Modulated Signals
 IEEE COMM. LETTERS
, 2003
"... In this letter, we express the CramerRao Bound (CRB) for carrier phase estimation from a noisy linearly modulated signal with encoded data symbols, in terms of the marginal a posteriori probabilities (APPs) of the coded symbols. For a wide range of classical codes (block codes, convolutional codes, ..."
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Cited by 12 (8 self)
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In this letter, we express the CramerRao Bound (CRB) for carrier phase estimation from a noisy linearly modulated signal with encoded data symbols, in terms of the marginal a posteriori probabilities (APPs) of the coded symbols. For a wide range of classical codes (block codes, convolutional codes, and trelliscoded modulation), these marginal APPs can be computed efficiently by means of the BahlCockeJelinkeRaviv (BCJR) algorithm, whereas for codes that involve interleaving (turbo codes and bit interleaved coded modulation), iterated application of the BCJR algorithm is required. Our numerical results show that when the BER of the coded system is less than about 10 3 , the resulting CRB is essentially the same as when transmitting a training sequence.