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57
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.
Precoding in MultiAntenna and MultiUser Communications
"... In this paper, TomlinsonHarashima precoding for multipleinput/multipleoutput systems including multipleantenna and multiuser systems is studied. It is shown that nonlinear preequalization offers significant advantages over linear preequalization which increases average transmit power. Moreover ..."
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Cited by 102 (2 self)
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In this paper, TomlinsonHarashima precoding for multipleinput/multipleoutput systems including multipleantenna and multiuser systems is studied. It is shown that nonlinear preequalization offers significant advantages over linear preequalization which increases average transmit power. Moreover, it outperforms decisionfeedback equalization at the receiver side which is applicable if joint processing at the receiver side is possible, and which suffers from error propagation. A number of aspects of practical importance are studied. Loading, i.e., the optimum distribution of transmit power and rate is discussed in detail. It is shown that the capacity of the underlying MIMO channel can be utilized asymptotically by means of nonlinear precoding.
On the construction of some capacityapproaching coding schemes
, 2000
"... This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint source ..."
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Cited by 82 (2 self)
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This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint sourcechannel coding schemes. We first show some examples of sources and channels where no coding is optimal for all values of the signaltonoise ratio (SNR). When the source bandwidth is greater than the channel bandwidth, joint coding schemes based on spacefilling curves and other families of curves are proposed. For uniform sources and modulo channels, our coding scheme based on spacefilling curves operates within 1.1 dB of Shannon’s ratedistortion bound. For Gaussian sources and additive white Gaussian noise (AWGN) channels, we can achieve within 0.9 dB of the ratedistortion bound. The second scheme is based on lowdensity paritycheck (LDPC) codes. We first demonstrate that we can translate threshold values of an LDPC code between channels accurately using a simple mapping. We develop some models for density evolution
The wiretap channel with feedback: Encryption over the channel
 IEEE TRANS. INF. THEORY
, 2008
"... In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feedforward and feedback signals share the same noisy channel in the present model ..."
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Cited by 59 (8 self)
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In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feedforward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless moduloadditive channel with a fullduplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source–destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the halfduplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source–wiretapper channel is less noisy than the source–destination channel) is proposed. These results hinge on the moduloadditive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.
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.
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.
Coded modulation using superimposed binary codes
 IEEE Trans. Inform. Theory
, 2004
"... Abstract—In this correspondence, we investigate in a comprehensive fashion a onelayer coding/shaping scheme resembling a perfectly cooperated multipleaccess system. At the transmitter, binary data are encoded by either singlelevel or multilevel codes. The coded bits are first randomly interleaved ..."
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Cited by 34 (14 self)
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Abstract—In this correspondence, we investigate in a comprehensive fashion a onelayer coding/shaping scheme resembling a perfectly cooperated multipleaccess system. At the transmitter, binary data are encoded by either singlelevel or multilevel codes. The coded bits are first randomly interleaved and then entered into a signal mapper. At each time, the signal mapper accepts as input multiple binary digits and delivers as output an amplitude signal, where the input are first independently mapped into 2PAM signals (possibly having different amplitudes) and then superimposed to form the output. The receiver consists of an iterative decoding/demapping algorithm with an entropybased stopping criterion. In the special cases when all the 2PAM signals have equal amplitudes, based on an irregular trellis, we propose an optimal softinput–softoutput (SISO) demapping algorithm with quadratic rather than exponential complexity. In the general cases, when multilevel codes are employed, we propose powerallocation strategies to facilitate the iterative decoding/dempaping algorithm. Using the unequal powerallocations and the Gaussianapproximationbased suboptimal demapping algorithm (with linear complexity), coded modulation with high bandwidth efficiency can be implemented. Index Terms—Coded modulation, coding/shaping scheme, iterative decoding/demapping algorithm, iterative multistage decoding, multilevel coding, sigmamapping, softinput–softoutput (SISO) demapping algorithm. I.
Joint WynerZiv/DirtyPaper Coding by ModuloLattice Modulation
"... The combination of source coding with decoder sideinformation (WynerZiv problem) and channel coding with encoder sideinformation (Gel’fandPinsker problem) can be optimally solved using the separation principle. In this work we show an alternative scheme for the quadraticGaussian case, which mer ..."
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Cited by 15 (2 self)
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The combination of source coding with decoder sideinformation (WynerZiv problem) and channel coding with encoder sideinformation (Gel’fandPinsker problem) can be optimally solved using the separation principle. In this work we show an alternative scheme for the quadraticGaussian case, which merges source and channel coding. This scheme achieves the optimal performance by a applying modulolattice modulation to the analog source. Thus it saves the complexity of quantization and channel decoding, and remains with the task of “shaping” only. Furthermore, for high signaltonoise ratio (SNR), the scheme approaches the optimal performance using an SNRindependent encoder, thus it is robust to unknown SNR at the encoder.
On Error Exponents of Modulo Lattice Additive Noise Channels
 IEEE Trans. on Information Theory
, 2006
"... Modulo lattice additive noise (MLAN) channels appear in the analysis of structured binning codes for Costa’s dirtypaper channel and of nested lattice codes for the additive white Gaussian noise (AWGN) channel. In this paper, we derive a new lower bound on the error exponents of the MLAN channel. Wi ..."
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Cited by 14 (2 self)
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Modulo lattice additive noise (MLAN) channels appear in the analysis of structured binning codes for Costa’s dirtypaper channel and of nested lattice codes for the additive white Gaussian noise (AWGN) channel. In this paper, we derive a new lower bound on the error exponents of the MLAN channel. With a proper choice of the shaping lattice and the scaling parameter, the new lower bound coincides with the randomcoding lower bound on the error exponents of the AWGN channel at the same signaltonoise ratio (SNR) in the spherepacking and straightline regions. This result implies that, at least for rates close to channel capacity, (1) writing on dirty paper is as reliable as writing on clean paper; and (2) lattice encoding and decoding suffer no loss of error exponents relative to the optimal codes (with maximumlikelihood decoding) for the AWGN channel. Keywords: Additive white Gaussian noise channel, Costa’s dirtypaper channel, error exponents, lattice decoding, modulo lattice additive noise channel, nested lattice codes
Nearcapacity coding in multicarrier modulation systems
 IEEE TRANSACTIONS ON COMMUNICATIONS
, 2004
"... We apply irregular lowdensity paritycheck (LDPC) codes to the design of multilevel coded quadrature amplitude modulation (QAM) schemes for application in discrete multitone systems in frequencyselective channels. A combined Gray/Ungerboeck scheme is used to label each QAM constellation. The Gray ..."
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Cited by 12 (4 self)
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We apply irregular lowdensity paritycheck (LDPC) codes to the design of multilevel coded quadrature amplitude modulation (QAM) schemes for application in discrete multitone systems in frequencyselective channels. A combined Gray/Ungerboeck scheme is used to label each QAM constellation. The Graylabeled bits are protected using an irregular LDPC code with iterative softdecision decoding, while other bits are protected using a highrate Reed–Solomon code with harddecision decoding (or are left uncoded). The rate of the LDPC code is selected by analyzing the capacity of the channel seen by the Graylabeled bits and is made adaptive by selective concatenation with an inner repetition code. Using a practical bitloading algorithm, we apply this coding scheme to an ensemble of frequencyselective channels with Gaussian noise. Over a large number of channel realizations, this coding scheme provides an average effective coding gain of more than 7.5 dB at a biterror rate of 10 7 and a block length of approximately 10 5 b. This represents a gap of approximately 2.3 dB from the Shannon limit of the additive white Gaussian noise channel, which could be closed to within 0.8–1.2 dB using constellation shaping.