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64
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.
Multilevel Codes: Theoretical Concepts and Practical Design Rules
, 1999
"... This paper deals with 2 ` ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a ..."
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Cited by 206 (33 self)
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This paper deals with 2 ` ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a large space of rate combinations such that MLC and full maximumlikelihood decoding (MLD) can approach capacity. It is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of MLD. The capacity rule, the balanced distances rules, and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design. Simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies. Moreover, topics relevant in practical applications such as signal set labeling, dimensional...
Adaptive Multidimensional Coded Modulation Over Flat Fading Channels
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2000
"... We introduce a general adaptive coding scheme for Nakagami multipath fading channels. An instance of the coding scheme utilizes a set of 2 dimensional (2 D) trellis codes originally designed for additive white Gaussian noise (AWGN) channels. Any set of 2 D trellis codes for AWGN channels can be u ..."
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Cited by 62 (16 self)
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We introduce a general adaptive coding scheme for Nakagami multipath fading channels. An instance of the coding scheme utilizes a set of 2 dimensional (2 D) trellis codes originally designed for additive white Gaussian noise (AWGN) channels. Any set of 2 D trellis codes for AWGN channels can be used. Sets for which all codes can be generated by the same encoder and decoded by the same decoder are of particular interest. A feedback channel between the transmitter and receiver makes it possible to transmit at high spectral efficiencies under favorable channel conditions and respond to channel degradation through a smooth reduction of the spectral efficiency. We develop a general technique to determine the average spectral efficiency of the coding scheme for any set of 2 D trellis codes. As an illustrative example, we calculate the average spectral efficiency of an adaptive codec utilizing eight 4D trellis codes. The example codec is based on the International Telecommunications Union's ITUT V.34 modem standard.
New Trellis Codes Based on Lattices and Cosets
, 1987
"... A new technique is proposed for constructing trellis codes, which provides an alternative to Ungerboeck’s method of “set partitioning.” The new codes use a signal constellation consisting of points,from an ndimensional lattice A, with an equal number of hints from each coset of a sublattice A’. On ..."
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Cited by 47 (7 self)
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A new technique is proposed for constructing trellis codes, which provides an alternative to Ungerboeck’s method of “set partitioning.” The new codes use a signal constellation consisting of points,from an ndimensional lattice A, with an equal number of hints from each coset of a sublattice A’. One part of the input stream drives a generalized convolutional code whose outputs are co&s of A’, while the other part selects points from these cosets. Several of the new codes are better than those previously known.
Coset codes–Part I: Introduction and geometrical classification
 IEEE Transactions on Information Theory
, 1988
"... AbstractPractically all known good constructive coding techniques for ..."
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Cited by 44 (0 self)
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AbstractPractically all known good constructive coding techniques for
Fractionally spaced equalizers
 IEEE Signal Process. Mag
, 1996
"... odern digital transmission systems commonly use an adaptive equalizer as a key part of the receiver. The design of this equalizer is important since it determines the maximum quality attainable from the system, and represents a high fraction of the computation used to implement the demodulator. Rece ..."
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Cited by 14 (0 self)
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odern digital transmission systems commonly use an adaptive equalizer as a key part of the receiver. The design of this equalizer is important since it determines the maximum quality attainable from the system, and represents a high fraction of the computation used to implement the demodulator. Recent analytical results offer a new way of looking at fractionally spaced equalizers and have some surprising practical implications. This article describes the data communications problem, the rationale for introducing fractionally spaced equalizers, the new results, and their implications. We then apply those results to actual transmission channels. Overview “The revolution in data communication technology can be dated from the invention of automatic and adaptive channel equalization in the late 1960s ” [6] (sidebar A). Indeed, sophisticated communications systems such as quadrature amplitude modulation (QAM) were developed to increase the bitsperHertz ratio for transmission. First introduced for voiceband modems [21], the technology was then applied to microwave radio relay systems [5]. Its success in those applications has led to great interest in its use for other communication situations, where economic or regulatory considerations limit the available transmission bandwidth. An important example of such an application is the wireless and cable distribution of digital television [14]. Central to the successful employment of QAM transmison a realistic tranwiission 5ystcm 14 the use of udclptive 5 equalization to counteract the disruptive effects of the cif: nal’4 propagation from the transmitter to the receiver. The equaliler’s importance, coupled with the fact that it tends to
LogConcavity Property of the Error Probability with Application to Local Bounds for Wireless Communications
, 710
"... Abstract — A clear understanding the behavior of the error probability (EP) as a function of signaltonoise ratio (SNR) and other system parameters is fundamental for assessing the design of digital wireless communication systems. We propose an analytical framework based on the logconcavity proper ..."
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Cited by 8 (2 self)
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Abstract — A clear understanding the behavior of the error probability (EP) as a function of signaltonoise ratio (SNR) and other system parameters is fundamental for assessing the design of digital wireless communication systems. We propose an analytical framework based on the logconcavity property of the EP which we prove for a wide family of multidimensional modulation formats in the presence of Gaussian disturbances and fading. Based on this property, we construct a class of local bounds for the EP that improve known generic bounds in a given region of the SNR and are invertible, as well as easily tractable for further analysis. This concept is motivated by the fact that communication systems often operate with performance in a certain region of interest (ROI) and, thus, it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all SNRs. We present a possible application of these local bounds, but their relevance is beyond the example made in this paper. Index Terms — Error statistics, fading channels, local bounds, logconcavity, performance evaluation, probability. I.
Multidimensional mappings for iteratively decoded BICM on multiple antenna channel
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2005
"... ..."
Optimization of signal sets for partial response channelsPart I: Numerical techniques
 IEEE Trans. Inform. Theory
, 1991
"... AbstractFor a linear, timeinvariant, discretetime channel with transfer function H(f), and information rate R bits/T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2RK inputs of length K that maximizes the minimum 1, distance between pairs of outputs. ..."
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Cited by 6 (3 self)
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AbstractFor a linear, timeinvariant, discretetime channel with transfer function H(f), and information rate R bits/T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2RK inputs of length K that maximizes the minimum 1, distance between pairs of outputs. This paper studies the minimum distance between outputs, or equivalently, the coding gain of optimal signal sets as K +m. For large K this coding gain, relative to singlestep detection, can approximately be decomposed into the coding gain of an optimal signal set of length K for the identity channel, plus the gain of a “baseline ” coding scheme for the channel H(f). The baseline signal set is selected from the multidimensional integer lattice, where the basis vectors of the space are taken to be the eigenvectors of H‘H, and H is the Toeplitz matrix that maps channel inputs to channel outputs. The coding gain of the baseline scheme can be computed explicitly as K +CO in terms of IH(f)l and R. The minimum distance between channel outputs for optimal signal sets as K $ m is determined by the €rate of the channel. Existing upper and lower bounds on the erate are used to compute bounds on the maximum asymptotic coding gains achievable for some partial response channels. These asymptotic coding gains are compared with the coding gains corresponding to signal sets found by numerical optimization techniques. A comparison of bounds on rrates for the identity and 1 D channels indicates that for a given large K, the squared minimum distance of an optimal signal set for the 1 D channel is 2 dB more than the squared minimum distance of an optimal signal set for the identity channel at a rate of 1 bit / T. For rates greater than 2 bits / T, however, this comparison indicates that optimal signal sets of length K for these two channels have nearly the same minimum distance. Index TermsCoding, partialresponse channels, intersymbol interference, crate, multidimensional signal sets.
Lineartime nearest point algorithms for Coxeter lattices
, 2009
"... The Coxeter lattices, which we denote An/m, are a family of lattices containing many of the important lattices in low dimensions. This includes An, E7, E8 and their duals A ∗ n, E ∗ 7 and E ∗ 8. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, ..."
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Cited by 4 (2 self)
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The Coxeter lattices, which we denote An/m, are a family of lattices containing many of the important lattices in low dimensions. This includes An, E7, E8 and their duals A ∗ n, E ∗ 7 and E ∗ 8. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexity O(n log n) and the other with worst case complexity O(n) where n is the dimension of the lattice. We show that for the particular lattices An and A ∗ n the algorithms reduce to simple nearest point algorithms that already exist in the literature.