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An Algebraic Approach to PhysicalLayer Network Coding
 IEEE TRANS. INFORM. THEORY
, 2010
"... The problem of designing new physicallayer network coding (PNC) schemes via lattice partitions is considered. Building on recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using informationtheoretic tools, we take an algebraic approach to show its potential in nonasymptotic ..."
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Cited by 41 (4 self)
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The problem of designing new physicallayer network coding (PNC) schemes via lattice partitions is considered. Building on recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using informationtheoretic tools, we take an algebraic approach to show its potential in nonasymptotic settings. We first relate NazerGastpar’s approach to the fundamental theorem of finitely generated modules over a principle ideal domain. Based on this connection, we generalize their code construction and simplify their encoding and decoding methods. This not only provides a transparent understanding of their approach, but more importantly, it opens up the opportunity to design efficient and practical PNC schemes. Finally, we apply our framework to the Gaussian relay network and demonstrate its advantage over conventional PNC schemes.
Lattice decoding for the computeandforward protocol
 In Third International Conference on Communications and Networking
"... Abstract—In this work we focus exclusively on the ComputeandForward (C&F) protocol as a channel codingbased approach for Physical Layer Network Coding. The Core principle of this relaying strategy is based on using Nested Lattice Codes. The source nodes in a relay network encode their messag ..."
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Abstract—In this work we focus exclusively on the ComputeandForward (C&F) protocol as a channel codingbased approach for Physical Layer Network Coding. The Core principle of this relaying strategy is based on using Nested Lattice Codes. The source nodes in a relay network encode their messages into lattice codewords and transmit them to the relay. The latter receives a noisy mixing of these codewords and decodes an integer linear combination of them for sequential transmission. To the best of our knowledge, all existent works related to the ComputeandForward protocol study only its theoretical limits and no experimental analysis has been proposed so far. Our contribution through this work concerns a plethora of practical aspects, related to lattice decoding for the C&F, that need to be solved to achieve the promising potential of this strategy. We propose practical decoding approaches and investigate the achieved diversity order and identify the relevant parameters that may influence it. We provide simulation results to compare the performance of the different proposed decoding approaches and to link theoretical results with practical aspects.
Multistage computeandforward with multilevel lattice codes based on product constructions
 in Proc. IEEE ISIT
, 2014
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On the Ergodic Rate for ComputeandForward
"... Abstract—A key issue in computeandforward for physical layer network coding scheme is to determine a good function of the received messages to be reliably estimated at the relay nodes. We show that this optimization problem can be viewed as the problem of finding the closest point of Z[i] n to a l ..."
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Cited by 4 (4 self)
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Abstract—A key issue in computeandforward for physical layer network coding scheme is to determine a good function of the received messages to be reliably estimated at the relay nodes. We show that this optimization problem can be viewed as the problem of finding the closest point of Z[i] n to a line in the ndimensional complex Euclidean space, within a bounded region around the origin. We then use the complex version of the LLL lattice basis reduction (CLLL) algorithm to provide a reduced complexity suboptimal solution as well as an upper bound to the minimum distance of the lattice point from the line. Using this bound we are able to find a lower bound to the ergodic rate and a union bound estimate on the error performance of a lattice constellation used for lattice network coding. We compare performance of the CLLL with a more complex iterative optimization method as well as with a simple quantized search. Simulations show how CLLL can trade some performance for a lower complexity. Index Terms—Ergodic rate, computeandforward, CLLL algorithm, quantized error, successive refinement. 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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Cited by 4 (2 self)
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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.
Phase Precoding for the ComputeandForward Protocol,” submitted for possible publication Available online at: http://arxiv.org/abs/1404.4157.282
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How Sensitive is ComputeandForward to Channel Estimation Errors?
"... Abstract—We investigate the sensitivity of ComputeandForward (C&F) to channel estimation errors. More specifically, a general formula for the computation rate region of a C&F relay, suffering from imperfect channel estimation, is derived, which is then tightly approximated for Gaussian dis ..."
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Abstract—We investigate the sensitivity of ComputeandForward (C&F) to channel estimation errors. More specifically, a general formula for the computation rate region of a C&F relay, suffering from imperfect channel estimation, is derived, which is then tightly approximated for Gaussian distributed channel estimation errors. Furthermore, a closedform expression for the distribution of the C&F rate loss is presented, which can be efficiently used to compute relevant statistical parameters, such as the mean rate loss. Numerical and simulation results highlight the high sensitivity of the overall network performance to channel estimation errors. I.