| 191. |
- Mitchell, David G.M., et al.
(författare)
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Spatially Coupled LDPC Codes Constructed From Protographs
- 2015
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 61:9, s. 4866-4889
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we construct protograph-based spatially coupled low-density parity-check (LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary L. We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large L, the BP thresholds on both the binary erasure channel and the binary-input additive white Gaussian noise channel saturate to a particular value significantly better than the BP decoding threshold and numerically indistinguishable from the optimal maximum a posteriori decoding threshold of the uncoupled LDPC code. When all variable nodes in the coupled chain have degree greater than two, asymptotically the error probability converges at least doubly exponentially with decoding iterations and we obtain sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit. Further, the gap to capacity decreases as the density of the graph increases, opening up a new way to construct capacity achieving codes on memoryless binary-input symmetric-output channels with low-complexity BP decoding.
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| 192. |
- Mohammed, Saif Khan, 1977-, et al.
(författare)
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MIMO Precoding with X- and Y- Codes
- 2011
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Ingår i: IEEE Transactions on Information Theory. - New Jersey, USA : IEEE. - 0018-9448 .- 1557-9654. ; 57:6, s. 3542-3566
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Tidskriftsartikel (refereegranskat)abstract
- We consider a slow fading nt x nr multiple-input multiple-output (MIMO) system with channel state information (CSI) at both the transmitter and receiver. Since communication in such scenarios is subject to block fading, reception reliability, quantified in terms of the achievable diversity gain, is of importance. A simple and well known precoding scheme is based upon the singular value decomposition (SVD) of the channel matrix, which transforms the MIMO channel into parallel subchannels. Despite having low maximum likelihood decoding (MLD) complexity, this SVD based precoding scheme provides a diversity gain which is limited by the diversity gain of the weakest subchannel. We therefore propose X- and YCodes, which improve the diversity gain of the SVD precoding scheme, by jointly coding information across a pair of subchannels (i.e., pairing subchannels). In particular, subchannels with high diversity gain are paired with those having low diversitygain. A pair of subchannels is jointly encoded using a 2 x 2 real matrix, which is fixed a priori and does not change with each channel realization. For X-Codes, these matrices are 2-dimensional rotation matrices parameterized by a single angle, while for Y-Codes, these matrices are 2-dimensional upper left triangular matrices. Also, since joint coding is performed only across a pair of subchannels, the joint MLD complexity remains low. In particular, the MLD complexity of Y-Codes is even lower than that of X-Codes, and is equivalent to symbol by symbol detection. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but with encoding matrices adapted to each channel realization. With respect to the error probability performance, the optimal encoding matrices for X-, YCodes/ Precoders are derived analytically and numerically. Whencompared to other precoding schemes reported in the literature, it is observed that X-Codes/Precoders perform better in wellconditioned channels, while Y-Codes/Precoders perform better in ill-conditioned channels.
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| 193. |
- Mohammed, Saif Khan, 1977-, et al.
(författare)
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Precoding by Pairing Subchannels to Increase MIMO Capacity with Discrete Input Alphabets
- 2011
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Ingår i: IEEE Transactions on Information Theory. - New Jersey, USA : IEEE. - 0018-9448 .- 1557-9654. ; 57:7, s. 4156-4169
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Tidskriftsartikel (refereegranskat)abstract
- We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on the X-Codes in \cite{Xcodes_paper} to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and a $2\times 2$ real rotation matrix for each pair (parameterized with a single angle). This precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is solved by {\em i}) optimizing the rotation angle and the power allocation within each pair and {\em ii}) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz {\em et al.}, and is significantly better than Mercury/waterfilling strategy by Lozano {\em et al.}. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.
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| 194. |
- Moloudi, Saeedeh, et al.
(författare)
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Spatially Coupled Turbo-Like Codes
- 2017
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 63:10, s. 6199-6215
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we introduce the concept of spatially coupled turbo-like codes (SC-TCs) as the spatial coupling of a number of turbo-like code ensembles. In particular, we consider the spatial coupling of parallel concatenated codes, introduced by Berrou et al., and that of serially concatenated codes (SCCs), introduced by Benedetto et al. Furthermore, we propose two extensions of braided convolutional codes (BCCs), and a class of turbo-like codes which have an inherent spatially coupled structure, to higher coupling memories, and show that these yield improved belief propagation (BP) thresholds as compared with the original BCC ensemble. We derive the exact density evolution (DE) equations for SC-TCs and analyze their asymptotic behavior on the binary erasure channel. We also consider the construction of families of rate-compatible SC-TC ensembles. Our numerical results show that the threshold saturation of the BP decoding threshold to the maximum a posteriori threshold of the underlying uncoupled ensembles occurs for large enough coupling memory. The improvement of the BP threshold is especially significant for SCCs and BCCs, whose uncoupled ensembles suffer from a poor BP threshold. For a wide range of code rates, SC-TCs show close-to-capacity performance as the coupling memory increases. We further give a proof of threshold saturation for SC-TC ensembles with identical component encoders. In particular, we show that the DE of SC-TC ensembles with identical component encoders can be properly rewritten as a scalar recursion. This allows us to define potential functions and prove threshold saturation using the proof technique recently introduced by Yedla et al.
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| 195. |
- Morgenshtern, Veniamin I., et al.
(författare)
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Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka’s Theorem
- 2013
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 59:7, s. 4213-4229
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Tidskriftsartikel (refereegranskat)abstract
- We find the capacity pre-log of a temporally correlatedRayleigh block-fading single-input multiple-output (SIMO)channel in the noncoherent setting. It is well known that for blocklength $L$ and rank of the channel covariance matrix equal to $Q$, the capacity pre-log in the single-input single-output (SISO) case is given by $1-Q/L$. Here, $Q/L$ can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to $1/L$ and can, hence, be made to vanish for the blocklength$L\to\infty$, even if $Q/L$ remains constant as $L\to\infty$. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna’s channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka’s Theorem on the Resolution of Singularities.
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| 196. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Joint Constellation Design for Noncoherent MIMO Multiple-Access Channels
- 2022
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 68:11, s. 7281-7305
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Tidskriftsartikel (refereegranskat)abstract
- We consider the joint constellation design problem for the noncoherent multiple-input multiple-output multiple-access channel (MAC). By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to minimize the error probability. As a baseline approach, we adapt several existing design criteria for the point-to-point channel to the MAC. Furthermore, we propose new design criteria. Our first proposed design metric is the dominating term in nonasymptotic lower and upper bounds on the pairwise error probability exponent. We give a geometric interpretation of the bound using Riemannian distance in the manifold of Hermitian positive definite matrices. From an analysis of this metric at high signal-to-noise ratio, we obtain further simplified metrics. For any given set of constellation sizes, the proposed metrics can be optimized over the set of constellation symbols. Motivated by the simplified metric, we propose a simple constellation construction consisting in partitioning a single-user constellation. We also provide a generalization of our previously proposed construction based on precoding individual constellations of lower dimensions. For a fixed joint constellation, the design metrics can be further optimized over the per-user transmit power, especially when the users transmit at different rates. Considering unitary space-time modulation, we investigate the option of building each individual constellation as a set of truncated unitary matrices scaled by the respective transmit power. Numerical results show that our proposed metrics are meaningful, and can be used as objectives to generate constellations through numerical optimization that perform better, for the same transmission rate and power constraint, than a common pilot-based scheme and the constellations optimized with existing metrics.
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| 197. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Unsourced Multiple Access With Random User Activity
- 2023
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 69:7, s. 4537-4558
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Tidskriftsartikel (refereegranskat)abstract
- To account for the massive uncoordinated random access scenario, which is relevant for the Internet of Things, Polyanskiy (2017) proposed a novel formulation of the multiple-access problem, commonly referred to as unsourced multiple access, where all users employ a common codebook and the receiver decodes up to a permutation of the messages. In this paper, we extend this seminal work to the case where the number of active users is random and unknown a priori. We define a random-access code accounting for both misdetection (MD) and false alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA probabilities. It suggests that the lack of knowledge of the number of active users entails a small penalty in energy efficiency when the target MD and FA probabilities are high. However, as the target MD and FA probabilities decrease, the energy efficiency penalty becomes more significant. For example, in a typical IoT scenario with framelength 19200 complex channel uses and 25–300 active users in average, the required energy per bit to achieve both MD and FA probabilities below 10-1, predicted by our bound, is only 0.5–0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. This gap increases to 3–4 dB when the target MD probability and/or FA probability is below 10-3. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of slotted-ALOHA with multi-packet reception, of a decoder that simply treats interference as noise, and of some recently proposed unsourced multiple access schemes. Numerical results suggest that, when the target MD and FA probabilities are high, it is effective to estimate the number of active users, then treat this estimate as the true value, and use a coding scheme that performs well for the case of known number of active users. However, this approach becomes energy inefficient when the requirements on MD and FA probabilities are stringent.
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| 198. |
- Nguyen, Khoa D., et al.
(författare)
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A tight lower bound to the outage probability of discrete-input block-fading channels
- 2007
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 53:11, s. 4314-4322
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Tidskriftsartikel (refereegranskat)abstract
- In this correspondence, a tight lower hound to the outage probability of discrete-input Nakagami-m block-fading channels is proposed. The approach permits an efficient method for numerical evaluation of the bound, providing an additional tool for system design. The optimal rate-diversity tradeoff for the Nakagami-m, block-fading channel is also derived and a tight upper bound is obtained for the optimal coding gain constant.
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| 199. |
- Nguyen, K. D., et al.
(författare)
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MIMO ARQ with multibit feedback : Outage analysis
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 58:2, s. 765-779
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Tidskriftsartikel (refereegranskat)abstract
- This paper studies the asymptotic outage performance of incremental redundancy automatic-repeat-request (INR-ARQ) transmission over multiple-input multiple-output (MIMO) block-fading channels with discrete input constellations. We first show that transmission with random codes using a discrete signal constellation across all transmit antennas achieves the optimal outage diversity given by the Singleton bound. The optimal SNR-exponent and outage diversity of INR-ARQ transmission over the MIMO block-fading channel are then analysed. We show that a significant gain in outage diversity is obtained by providing more than one bit feedback at each ARQ round. Thus, the outage performance of INR-ARQ transmission can be remarkably improved with minimal additional overhead. A practical feedback-and-power-adaptation rule is proposed for MIMO INR-ARQ, demonstrating the benefits provided by multibit feedback. Although the rule is sub-optimal in terms of outage performance, it achieves the optimal outage diversity.
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| 200. |
- Nguyen, Khoa D., et al.
(författare)
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Outage Exponents of Block-Fading Channels With Power Allocation
- 2010
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 56:5, s. 2373-2381
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Tidskriftsartikel (refereegranskat)abstract
- Power allocation is studied for fixed-rate transmission over block-fading channels with arbitrary continuous fading distributions and perfect transmitter and receiver channel state information. Both short-and long-term power constraints for arbitrary input distributions are considered. Optimal power allocation schemes are shown to be direct applications of previous results in the literature. It is shown that the short-and long-term outage exponents for arbitrary input distributions are related through a simple formula. The formula is useful to predict when the delay-limited capacity is positive. Furthermore, this characterization is useful for the design of efficient coding schemes for this relevant channel model.
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