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17
Precoded IntegerForcing Universally Achieves the MIMO Capacity to Within a Constant Gap
, 2013
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Integerforcing MIMO linear receivers based on lattice reduction
 IEEE Trans. Wireless Commun
, 2013
"... Abstract—A new architecture called integerforcing (IF) linear receiver has been recently proposed for multipleinput multipleoutput (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, ..."
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Abstract—A new architecture called integerforcing (IF) linear receiver has been recently proposed for multipleinput multipleoutput (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, we propose a method based on HermiteKorkineZolotareff (HKZ) and Minkowski lattice basis reduction algorithms to obtain the integer coefficients for the IF receiver. We show that the proposed method provides a lower bound on the ergodic rate, and achieves the full receive diversity. Suitability of complex LenstraLenstraLovasz (LLL) lattice reduction algorithm (CLLL) to solve the problem is also investigated. Furthermore, we establish the connection between the proposed IF linear receivers and lattice reductionaided MIMO detectors (with equivalent complexity), and point out the advantages of the former class of receivers over the latter. For the 2 × 2 and 4 × 4 MIMO channels, we compare the codedblock error rate and bit error rate of the proposed approach with that of other linear receivers. Simulation results show that the proposed approach outperforms the zeroforcing (ZF) receiver, minimum mean square error (MMSE) receiver, and the lattice reductionaided MIMO detectors. Index Terms—MIMO, integerforcing, lattice reduction, Minkowski reduction, HermiteKorkineZolotareff reduction, complex LenstraLenstraLovasz lattice reduction, linear receivers. I.
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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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.
Phase Precoding for the ComputeandForward Protocol,” submitted for possible publication Available online at: http://arxiv.org/abs/1404.4157.282
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ComputeandForward TwoWay Relaying
 IET Commun
"... In this paper, a new twoway relaying scheme based on computeandforward (CMF) framework and relay selection strategies is proposed, which provides a higher throughput than the conventional twoway relaying schemes. Two cases of relays with or without feedback transmission capability are considered ..."
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In this paper, a new twoway relaying scheme based on computeandforward (CMF) framework and relay selection strategies is proposed, which provides a higher throughput than the conventional twoway relaying schemes. Two cases of relays with or without feedback transmission capability are considered. An upper bound on the computation rate of each relay is derived, and based on that, a lower bound on the outage probability of the system is presented assuming block Rayleigh fading channels. Numerical results show that while the average sum rate of the system without feedback, named as Max ComputeandForward (MCMF), reaches the derived upper bound only in low SNRs, that of the system with feedback, named as Aligned ComputeandForward (ACMF) reaches the bound in all SNRs. However, both schemes approach the derived lower bound on the outage probability in all SNRs. For the ACMF, another power assignment based on applying the constraint on the total powers of both users rather than on the power of each separately, is introduced. The result shows that the ACMF performs better under the new constraint. Moreover, the numerical results show that the outage performance, average sum rate, and symbol error rate of the proposed schemes are significantly better than those of twostep and threestep decodeandforward (DF) and amplifyandforward (AF) strategies for the examples considered. Index Terms compute and forward, max computeandforward, aligned computeandforward, feedback, twoway relaying, relay selection, outage probability, average sum rate, symbol error rate. I
IntegerForcing Linear Receiver Design over MIMO Channels
, 2012
"... Motivated by recently presented integerforcing linear receiver architecture, we propose algorithms to design optimal integerforcing coefficient matrix such that the total achievable rate is maximized. ..."
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Motivated by recently presented integerforcing linear receiver architecture, we propose algorithms to design optimal integerforcing coefficient matrix such that the total achievable rate is maximized.
Weak secrecy in the multiway untrusted relay channel with computeandforward
 IEEE Trans. Inf. Forens. Sec
, 2015
"... We investigate the problem of secure communications in a Gaussian multiway relay channel applying the computeandforward scheme using nested lattice codes. All nodes employ halfduplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest b ..."
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We investigate the problem of secure communications in a Gaussian multiway relay channel applying the computeandforward scheme using nested lattice codes. All nodes employ halfduplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme. We start with the general case of the singleinput multipleoutput (SIMO) Luser multiway relay channel and provide an achievable secrecy rate region under a weak secrecy criterion. We show that the securely achievable sum rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. Particularly, we show that all nodes must encode their messages such that the common computation rate tuple falls outside the MAC capacity region of the relay. We provide results for the singleinput singleoutput (SISO) and the multipleinput singleinput (MISO) Luser multiway relay channel as well as the twoway relay channel. We discuss these results and show the dependency between channel realization and achievable secrecy rate. We further compare our result to available results in the literature for different schemes and show that the proposed scheme operates close to the computeandforward rate without secrecy.
Integer ForcingandForward Transceiver Design for MIMO MultiPair TwoWay Relaying
, 2014
"... In this paper, we propose a new transmission scheme, named as Integer ForcingandForward (IFF), for communications among multipair multipleantenna users in which each pair exchanges their messages with the help of a single multi antennas relay in the multipleaccess and broadcast phases. The prop ..."
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In this paper, we propose a new transmission scheme, named as Integer ForcingandForward (IFF), for communications among multipair multipleantenna users in which each pair exchanges their messages with the help of a single multi antennas relay in the multipleaccess and broadcast phases. The proposed scheme utilizes computeandforward (CMF) strategy and Integer Forcing Linear Receiver (IFLR) at relay, which uses equations, i.e., linear integercombinations of messages, to harness the intrapair interference. Accordingly, we propose the design of mean squared error (MSE) based transceiver, including precoder and projection matrices for the relay and users, assuming that the perfect channel state information (CSI) is available. In this regards, in the multipleaccess phase, we introduce two new MSE criteria for the related precoding and filter designs, i.e., the sum of the equations ’ MSE (SumEquation MSE) and the maximum of the equations ’ MSE (MaxEquation MSE), to exploit the equations in the relay. Moreover, in the broadcast phase, we use the two traditional MSE criteria, i.e. the sum of the users ’ mean squred errors (Sum MSE) and the maximum of the users ’ mean squared errors (Max MSE), to design the related precoding and filters for recovering relay’s equations in the users. Then, we consider a more practical scenario with imperfect CSI. For this case, IFLR receiver is modified, and another transceiver design is proposed, which take into account the effect of channels estimation error. We evaluate the performance of our proposed strategy and compare the results with the conventional amplifyandforward (AF) and decodeandforward (DF) strategies for the same scenario. The results
Full Diversity Unitary Precoded IntegerForcing
"... We consider a pointtopoint flatfading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lat ..."
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We consider a pointtopoint flatfading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lattice codeword is then multiplied by a unitary precoding matrix P and sent through the channel. At the receiver side, an integerforcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integerforcing (UPIF). We show that UPIF can achieve fulldiversity under a constraint based on the shortest vector of a lattice generated by the precoding matrix P. This constraint and a simpler version of that provide design criteria for two types of fulldiversity UPIF. Type I uses a unitary precoder that adapts at each channel realization. Type II uses a unitary precoder, which remains fixed for all channel realizations. We then verify our results by computer simulations in 2 × 2, and 4 × 4 MIMO using different QAM constellations. We finally show that the proposed Type II UPIF outperform the MIMO precoding Xcodes at high data rates.
Unitary Precoding for IntegerForcing MIMO Linear Receivers
 Proc. of IEEE Information Theory Workshop (ITW
, 2014
"... Abstract—A flat fading pointtopoint multipleantenna channel is considered where the channel state information is known at both transmitter and receiver. At the transmitter side, we use a lattice encoder to map information symbols to lattice codewords. The lattice coded layers are then precoded u ..."
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Abstract—A flat fading pointtopoint multipleantenna channel is considered where the channel state information is known at both transmitter and receiver. At the transmitter side, we use a lattice encoder to map information symbols to lattice codewords. The lattice coded layers are then precoded using unitary matrices satisfying nonvanishing minimum product distance. At the receiver side, an integerforcing linear receiver is employed. This scheme is called ‘unitary precoded integerforcing’. We show that by applying the proposed precoding technique fulldiversity can be achieved. We then verify this result by conducting computer simulations in a 2 × 2 and 4 × 4 multipleinput multipleoutput (MIMO) channel using fulldiversity algebraic rotation precoder matrices. Index Terms—IntegerForcing, unitary precoding, lattice codes, fulldiversity. I.