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70
Nested Linear/Lattice Codes for Structured Multiterminal Binning
, 2002
"... Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning sch ..."
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Cited by 352 (15 self)
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Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning scheme. Wyner and other researchers proposed various forms of coset codes for efficient binning, yet these schemes were applicable only for lossless source (or noiseless channel) network coding. To extend the algebraic binning approach to lossy source (or noisy channel) network coding, recent work proposed the idea of nested codes, or more specifically, nested paritycheck codes for the binary case and nested lattices in the continuous case. These ideas connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications. We review these recent developments and explore their tight relation to concepts such as combined shaping and precoding, coding for memories with defects, and digital watermarking. We also propose a few novel applications adhering to a unified approach.
Computeandforward: Harnessing interference through structured codes
 IEEE TRANS. INF. THEORY
, 2009
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Capacity of the Gaussian Twoway Relay Channel to within 1 2 Bit
, 902
"... In this paper, a Gaussian twoway relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in fullduplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested l ..."
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Cited by 103 (2 self)
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In this paper, a Gaussian twoway relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in fullduplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested lattice codes for the uplink and structured binning for the downlink. We show that the scheme achieves within 1 2 bit from the cutset bound for all channel parameters and becomes asymptotically optimal as the signal to noise ratios increase. Index Terms Twoway relay channel, wireless networks, network coding, lattice codes
Averaging bounds for lattices and linear codes
 IEEE Trans. Information Theory
, 1997
"... Abstract — General random coding theorems for lattices are derived from the Minkowski–Hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out. A new version of the Minkowski–Hlawka theorem itself is obtained as the limit, for p!1,ofa ..."
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Cited by 97 (1 self)
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Abstract — General random coding theorems for lattices are derived from the Minkowski–Hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out. A new version of the Minkowski–Hlawka theorem itself is obtained as the limit, for p!1,ofasimple lemma for linear codes over GF (p) used with plevel amplitude modulation. The relation between the combinatorial packing of solid bodies and the informationtheoretic “soft packing ” with arbitrarily small, but positive, overlap is illuminated. The “softpacking” results are new. When specialized to the additive white Gaussian noise channel, they reduce to (a version of) the de Buda–Poltyrev result that spherically shaped lattice codes and adecoder that is unaware of the shaping can achieve the rate 1=2 log2 (P=N).
Reliable physical layer network coding
 Proceedings of the IEEE
, 2011
"... Abstract—When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is ..."
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Cited by 55 (6 self)
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Abstract—When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routingbased strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear errorcorrecting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interferencelimited wireless networks. Index Terms—Digital communication, wireless networks, interference, network coding, channel coding, linear code, modulation, physical layer, fading, multiuser channels, multiple access, broadcast. I.
A Layered Lattice Coding Scheme for a Class of Three User Gaussian Interference Channels
 Allerton Conf. on Communication, Control, and Computing
, 2008
"... Abstract—The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an “alignment ” of the interference observed at each receiver. The layered lattice coding is shown to ach ..."
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Cited by 45 (4 self)
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Abstract—The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an “alignment ” of the interference observed at each receiver. The layered lattice coding is shown to achieve more than one degree of freedom for a class of interference channels and also achieves rates which are better than the rates obtained using the HanKobayashi coding scheme. I.
Lattices for distributed source coding: Jointly Gaussian sources and reconstruction of a linear function
 IEEE TRANSACTIONS ON INFORMATION THEORY, SUBMITTED
, 2007
"... Consider a pair of correlated Gaussian sources (X1, X2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear combination of X1 and X2 to within a meansquare distortion of ..."
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Cited by 45 (2 self)
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Consider a pair of correlated Gaussian sources (X1, X2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear combination of X1 and X2 to within a meansquare distortion of D. We obtain an inner bound to the optimal ratedistortion region for this problem. A portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components X1 and X2 first. This results in a better rate region for certain parameter values. Our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory. We then consider the case of linear reconstruction of K sources and provide an inner bound to the optimal ratedistortion region. Some parts of the inner bound are achieved using the following coding structure: lattice vector quantization followed by “correlated” latticestructured binning.
Lattices are Everywhere
"... As bees and crystals (and people selling oranges in the market) know it for many years, lattices provide efficient structures for packing, covering, quantization and channel coding. In the recent years, interesting links were found between lattices and coding schemes for multiterminal networks. Thi ..."
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Cited by 40 (3 self)
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As bees and crystals (and people selling oranges in the market) know it for many years, lattices provide efficient structures for packing, covering, quantization and channel coding. In the recent years, interesting links were found between lattices and coding schemes for multiterminal networks. This tutorial paper covers close to 20 years of my research in the area; of enjoying the beauty of lattice codes, and discovering their power in dithered quantization, dirty paper coding, WynerZiv DPCM, modulolattice modulation, distributed interference cancelation, and more. I.
Lowdensity lattice codes
 IEEE Transactions on Information Theory
, 2008
"... Abstract—Lowdensity lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. In LDLC a codeword x is generated directly at the ndimensional Euclidean space as a linear transformation of a correspondi ..."
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Cited by 33 (2 self)
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Abstract—Lowdensity lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. In LDLC a codeword x is generated directly at the ndimensional Euclidean space as a linear transformation of a corresponding integer message vector b, i.e., x = Gb, where H = G01 is restricted to be sparse. The fact that H is sparse is utilized to develop a lineartime iterative decoding scheme which attains, as demonstrated by simulations, good error performance within 0.5 dB from capacity at block length of n =100,000 symbols. The paper also discusses convergence results and implementation considerations. Index Terms—Iterative decoding, lattice codes, lattices, lowdensity paritycheck (LDPC) code. I.