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On complex LLL algorithm for integer forcing linear receivers
 in Proc. of 2013 Australian Communications Theory Workshop (AusCTW13
, 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.
Phase precoded computeandforward with partial feedback
"... Abstract—In this work, we propose phase precoding for the computeandforward (CoF) protocol. We derive the phase precoded computation rate and show that it is greater than the original computation rate of CoF protocol without precoder. To maximize the phase precoded computation rate, we need to ‘jo ..."
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Abstract—In this work, we propose phase precoding for the computeandforward (CoF) protocol. We derive the phase precoded computation rate and show that it is greater than the original computation rate of CoF protocol without precoder. To maximize the phase precoded computation rate, we need to ‘jointly ’ find the optimum phase precoding matrix and the corresponding network equation coefficients. This is a mixed integer programming problem where the optimum precoders should be obtained at the transmitters and the network equation coefficients have to be computed at the relays. To solve this problem, we introduce phase precoded CoF with partial feedback. It is a quantized precoding system where the relay jointly computes both a quasioptimal precoder from a finite codebook and the corresponding network equations. The index of the obtained phase precoder within the codebook will then be fedback to the transmitters. A “deep hole phase precoder ” is presented as an example of such a scheme. We further simulate our scheme with a lattice code carved out of the Gosset lattice and show that significant coding gains can be obtained in terms of equation error performance. Index Terms—Computeandforward, lattice codes, phase precoding. I.