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On Multiplicative Matrix Channels over Finite Chain Rings
"... Let R be a ring. A multiplicative matrix channel (MMC) over R is a communication channel in which the input X ∈ Rn× ` and the output Y ∈ Rm× ` are related by Y = AX, ..."
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Let R be a ring. A multiplicative matrix channel (MMC) over R is a communication channel in which the input X ∈ Rn× ` and the output Y ∈ Rm× ` are related by Y = AX,
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.
Full length article
, 1994
"... We quantize the angular momentum of the electromagnetic field in a linear medium. We consider the interaction of an atom with an evanescent wave. We discuss the transfer of angular momentum in such a wave in relation to some recent experiments. 1. ..."
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We quantize the angular momentum of the electromagnetic field in a linear medium. We consider the interaction of an atom with an evanescent wave. We discuss the transfer of angular momentum in such a wave in relation to some recent experiments. 1.
Network Coding Design in Wireless Cooperative Networks
, 2012
"... I would like to express my heartfelt gratitude and appreciation to my Postdoc advisor, Professor Wen Chen, for providing me this great opportunity to continue my research, also the endless encouragement, patience, guidance and research support throughout the postdoc period. Sincere appreciation goes ..."
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I would like to express my heartfelt gratitude and appreciation to my Postdoc advisor, Professor Wen Chen, for providing me this great opportunity to continue my research, also the endless encouragement, patience, guidance and research support throughout the postdoc period. Sincere appreciation goes to all the faculty and staff of Electronic Engineering Department, Shanghai Jiao Tong University (SJTU) for all kinds of academic and administrative helps. As an SJTU alumna who fulfills Bachelor, Master and now Postdoc, I have an abiding love of SJTU for providing firstclass education, cuttingedge scientific research and personality nurturing. My colleagues in Network Coding and Transmission Lab, Haibing Wan, Yang Yu,
10.1109/TCOMM.2015.2433293, IEEE Transactions on Communications 1 LDPC Codes for Networkcoded Bidirectional Relaying with Higher Order Modulation
"... Abstract—We study the use of LowDensity ParityCheck (LDPC) codes for twophase, networkcoded bidirectional relaying with higherorder modulation. In the multipleaccess phase, the sum of transmitted symbols scaled by the channel gains is the received relay constellation, which is networkmapped ..."
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Abstract—We study the use of LowDensity ParityCheck (LDPC) codes for twophase, networkcoded bidirectional relaying with higherorder modulation. In the multipleaccess phase, the sum of transmitted symbols scaled by the channel gains is the received relay constellation, which is networkmapped (clustered) to a transmit constellation for the ensuing broadcast phase. This operation at the relay is termed ClusteredScaledSum (CSS) decoding. We propose a CSS coding scheme for bidirectional relaying using a single LDPC code over a ring with higherorder PAM or QAM alphabets. We design a messagepassing decoder for CSS decoding with tradeoffs possible between complexity and performance. We suggest a method for completing a Constrained Partiallyfilled Latin Square (CPLS) to a latin square, which is used in the construction of network maps at the relay for any channel fading state. The performance of the CSS coding scheme with LDPC codes over rings is shown to be very close to informationtheoretic outer bounds. I.
LowDensity Lattice Codes for FullDuplex Relay Channels
"... Abstract—We propose a class of practical efficient lattice codes for realvalued fullduplex one and twoway relay channels. First, we investigate the problem from a theoretical perspective, proposing latticecoding instantiations of superposition block Markov encoding. Our encoding/decoding strat ..."
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Abstract—We propose a class of practical efficient lattice codes for realvalued fullduplex one and twoway relay channels. First, we investigate the problem from a theoretical perspective, proposing latticecoding instantiations of superposition block Markov encoding. Our encoding/decoding strategies recover the wellknown decodeandfoward rates for the oneway relay channel and a previouslyproven rate region for the twoway relay channel. Then, we construct practical, lowcomplexity implementations of these schemes using lowdensity lattice codes. Simulations show that our schemes achieve performance as close as 2.5 dB away from theoretical limits. Finally, we show that, due to features inherent to fullduplex relaying and practical codes, the gap to theoretical limits depends on the channel gains and transmit power of the relay relative to the source(s). We characterize this gap analytically, providing insight into the design of practical fullduplex relay systems. Index Terms—Lattice codes, relay networks, full duplex. I.
Design of Generalized Analog Network Coding for a MultipleAccess Relay Channel
, 2014
"... Abstract—In this paper, we propose a generalized analog network coding (GANC) scheme for a nonorthogonal multipleaccess relay channel (MARC), where two sources transmit their information simultaneously to the destination with the help of a relay. In the GANC scheme, the relay receives interfered ..."
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Abstract—In this paper, we propose a generalized analog network coding (GANC) scheme for a nonorthogonal multipleaccess relay channel (MARC), where two sources transmit their information simultaneously to the destination with the help of a relay. In the GANC scheme, the relay receives interfered signals from the two sources and generates signals to be transmitted with a relay function. We focus on the design of the optimal relay function to achieve the minimum pairwise error probability (PEP) of the system. Specifically, we first covert the relay function optimization problem to a transformation matrix (TM) design problem by presenting the received complex signals as signal matrices composed of real and imaginary parts. Then, we propose an optimization criteria, i.e., maximizing the minimal squared Euclidean distance (MMSED), to improve the PEP performance, since the PEP is determined by the Euclidean distance of the received constellation at destination. Next, we prove that the MMSED can be equivalently converted to a convex problem by introducing an intermediate matrix. We solve this convex problem by using the Lagrangian method and obtain the closedform expression of the optimal TM. We further improve the PEP performance by optimizing transmission power of the two sources. Simulation results show that the proposed GANC scheme has a better PEP performance compared to other alternative schemes. Index Terms—Relay function, multiple access relay channel, error probability, Euclidean distance. I.
Phase Precoded ComputeandForward with Partial Feedback
"... AbstractIn 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 &ap ..."
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AbstractIn 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 cor responding network equation coefficients. T his 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. T he 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 TermsComputeandforward, lattice codes, phase pre coding. I.
1On NonBinary Constellations for ChannelCoded PhysicalLayer Network Coding
"... Abstract—We investigate channelcoded physicallayer network coding in a twoway relaying scenario, where the end nodes A and B choose their symbols, SA and SB, from a small nonbinary field, F, and adopt a nonbinary PSK modulation. The relay then directly decodes the networkcoded combination aSA ..."
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Abstract—We investigate channelcoded physicallayer network coding in a twoway relaying scenario, where the end nodes A and B choose their symbols, SA and SB, from a small nonbinary field, F, and adopt a nonbinary PSK modulation. The relay then directly decodes the networkcoded combination aSA + bSB over F from the noisy received superimposed channelencoded packets. The advantage of working over nonbinary fields is that it offers the opportunity to decode according to multiple decoding coefficients (a, b). As only one of the networkcoded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of (a, b). In this paper, we compare different mappings between F and the PSK constellation, and prove that many have identical performance in terms of frame error rate (FER). Moreover, we derive a lower bound on the performance of decoding the networkcoded combinations. Simulation results show that if we adopt either i) concatenated ReedSolomon and convolutional coding or ii) lowdensity parity check codes, our nonbinary constellations can outperform the binary case significantly in the sense of minimizing the FER and, in particular, the ternary constellation has the best FER performance among all considered cases. Index Terms—Physicallayer network coding, nonbinary constellation mappers, outage probability, Reed Solomon Convolutional code concatenation, low density parity check code. I.
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.