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Lattice codes for the Gaussian relay channel: DecodeandForward and CompressandForward
, 2013
"... Lattice codes are known to achieve capacity in the Gaussian pointtopoint channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we show that ..."
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Lattice codes are known to achieve capacity in the Gaussian pointtopoint channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we show that lattice codes may be used to achieve the same performance as known i.i.d. Gaussian random coding techniques for the Gaussian relay channel, and show several examples of how this may be combined with the linearity of lattices codes in multisource relay networks. In particular, we present a nested lattice list decoding technique in which lattice codes are shown to achieve the decodeandforward (DF) rate of single source, single destination Gaussian relay channels with one or more relays. We next present two examples of how this DF scheme may be combined with the linearity of lattice codes to achieve new rate regions which for some channel conditions outperform analogous known Gaussian random coding techniques in multisource relay channels. That is, we derive a new achievable rate region for the twoway relay channel with direct links and compare it to existing schemes, and derive a new achievable rate region for the multiple access relay channel. We furthermore present a lattice compressandforward (CF) scheme for the Gaussian relay channel which exploits a lattice Wyner–Ziv binning scheme and achieves the same rate as the Cover–El Gamal CF rate evaluated for Gaussian random codes. These results suggest that structured/lattice codes may be used to mimic, and sometimes outperform, random Gaussian codes in general Gaussian networks.
Approximate ergodic capacity of a class of fading 2user 2hop networks
, 2012
"... We consider a fading AWGN 2user 2hop network in which the channel coefficients are independently and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity within a constant num ..."
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Cited by 5 (2 self)
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We consider a fading AWGN 2user 2hop network in which the channel coefficients are independently and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity within a constant number of bits/sec/Hz, independent of signaltonoise ratio. The achievability follows from the analysis of an interference neutralization scheme where the relays are partitioned into K pairs, and interference is neutralized separately by each pair of relays. For K =1, we previously proved a gap of 4 bits/sec/Hz for i.i.d. uniform phase fading and approximately 4.7 bits/sec/Hz for i.i.d. Rayleigh fading. In this paper, we give a result for general K. In the limit of large K, we characterize the ergodic sum capacity within 4((log π) − 1) ≃ 2.6 bits/sec/Hz for i.i.d. uniform phase fading and 4(4 − log 3π) ≃ 3.1 bits/sec/Hz for i.i.d. Rayleigh fading.
Multistage computeandforward with multilevel lattice codes based on product constructions
 in Proc. IEEE ISIT
, 2014
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Successive integerforcing and its sumrate optimality
 in 51th Annual Allerton Conference on Communications, Control, and Computing
, 2013
"... AbstractIntegerforcing receivers generalize traditional linear receivers for the multipleinput multipleoutput channel by decoding integerlinear combinations of the transmitted streams, rather then the streams themselves. Previous works have shown that the additional degree of freedom in choosi ..."
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Cited by 4 (1 self)
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AbstractIntegerforcing receivers generalize traditional linear receivers for the multipleinput multipleoutput channel by decoding integerlinear combinations of the transmitted streams, rather then the streams themselves. Previous works have shown that the additional degree of freedom in choosing the integer coefficients enables this receiver to approach the performance of maximumlikelihood decoding in various scenarios. Nonetheless, even for the optimal choice of integer coefficients, the additive noise at the equalizer's output is still correlated. In this work we study a variant of integerforcing, termed successive integerforcing, that exploits these noise correlations to improve performance. This scheme is the integerforcing counterpart of successive interference cancellation for traditional linear receivers. Similarly to the latter, we show that successive integerforcing is capacity achieving when it is possible to optimize the rate allocation to the different streams. In comparison to standard successive interference cancellation receivers, the successive integerforcing receiver offers more possibilities for capacity achieving rate tuples, and in particular, ones that are more balanced.
Structured Lattice Codes for Some TwoUser Gaussian Networks with Cognition, Coordination and Two Hops
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2013
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On Gaussian Interference Channels with Mixed Gaussian and Discrete Inputs
"... Abstract—This paper studies the sumrate of a class of memoryless, realvalued additive white Gaussian noise interference channels (IC) achievable by treating interference as noise (TIN). We develop and analytically characterize the rates achievable by a new strategy that uses superpositions of Gau ..."
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Abstract—This paper studies the sumrate of a class of memoryless, realvalued additive white Gaussian noise interference channels (IC) achievable by treating interference as noise (TIN). We develop and analytically characterize the rates achievable by a new strategy that uses superpositions of Gaussian and discrete random variables as channel inputs. Surprisingly, we demonstrate that TIN is sumgeneralized degrees of freedom optimal and can achieve to within an additive gap of O(1) or O(log log(SNR)) to the symmetric sumcapacity of the classical IC. We also demonstrate connections to other channels such as the IC with partial codebook knowledge and the block asynchronous IC. I.
On the Symmetric Kuser Interference Channels with Limited Feedback
, 2014
"... In this paper, we develop achievability schemes for symmetric Kuser interference channels with a ratelimited feedback from each receiver to the corresponding transmitter. We study this problem under two different channel models: the linear deterministic model, and the Gaussian model. For the deter ..."
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Cited by 2 (2 self)
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In this paper, we develop achievability schemes for symmetric Kuser interference channels with a ratelimited feedback from each receiver to the corresponding transmitter. We study this problem under two different channel models: the linear deterministic model, and the Gaussian model. For the deterministic model, the proposed scheme achieves a symmetric rate that is the minimum of the symmetric capacity with infinite feedback, and the sum of the symmetric capacity without feedback and the symmetric amount of feedback. For the Gaussian interference channel, we use lattice codes to propose a transmission strategy that incorporates the techniques of HanKobayashi message splitting, interference decoding, and decode and forward. This strategy achieves a symmetric rate which is within a constant number of bits to the minimum of the upper bound on the symmetric capacity with infinite feedback, and the sum of the upper bound on the symmetric capacity without feedback and the amount of symmetric feedback. This constant is obtained as a function of the number of users, K. The symmetric achievable rate is used to characterize the achievable generalized degrees of freedom which exhibits a gradual increase from no feedback to perfect feedback in the presence of feedback links with limited capacity.
4 Lattices from Codes for Harnessing Interference: An Overview and Generalizations
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