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Ram Zamir

Bio: Ram Zamir is an academic researcher from Tel Aviv University. The author has contributed to research in topics: Gaussian & Decoding methods. The author has an hindex of 37, co-authored 206 publications receiving 7437 citations. Previous affiliations of Ram Zamir include University of California, Santa Barbara & Massachusetts Institute of Technology.


Papers
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Journal ArticleDOI
TL;DR: Nested codes are proposed, or more specifically, nested parity-check codes for the binary case and nested lattices in the continuous case, which connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications.
Abstract: Network information theory promises high gains over simple point-to-point 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 (1974, 1978) 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, previous work proposed the idea of nested codes, or more specifically, nested parity-check 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 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.

1,008 citations

Journal ArticleDOI
Uri Erez1, Ram Zamir1
TL;DR: In this article, a lattice code with lattice decoding was proposed to achieve the additive white Gaussian noise (AWGN) channel capacity, whose effective noise is reduced by a factor of /spl radic/(1+SNR/SNR) for any desired nesting ratio.
Abstract: We address an open question, regarding whether a lattice code with lattice decoding (as opposed to maximum-likelihood (ML) decoding) can achieve the additive white Gaussian noise (AWGN) channel capacity We first demonstrate how minimum mean-square error (MMSE) scaling along with dithering (lattice randomization) techniques can transform the power-constrained AWGN channel into a modulo-lattice additive noise channel, whose effective noise is reduced by a factor of /spl radic/(1+SNR/SNR) For the resulting channel, a uniform input maximizes mutual information, which in the limit of large lattice dimension becomes 1/2 log (1+SNR), ie, the full capacity of the original power constrained AWGN channel We then show that capacity may also be achieved using nested lattice codes, the coarse lattice serving for shaping via the modulo-lattice transformation, the fine lattice for channel coding We show that such pairs exist for any desired nesting ratio, ie, for any signal-to-noise ratio (SNR) Furthermore, for the modulo-lattice additive noise channel lattice decoding is optimal Finally, we show that the error exponent of the proposed scheme is lower bounded by the Poltyrev exponent

839 citations

Journal ArticleDOI
TL;DR: The results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels.
Abstract: We consider the generalized dirty-paper channel Y=X+S+N,E{X/sup 2/}/spl les/P/sub X/, where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint P/sub X/, these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1/2log(2/spl pi/e/12)/spl ap/ 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1/2log2/spl pi/eG(/spl Lambda/), where G(/spl Lambda/) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels.

504 citations

Journal ArticleDOI
TL;DR: In this paper, the authors define an ensemble of lattices, and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings, sphere coverings, additive white Gaussian noise (AWGN) channel codes and mean-squared error quantization codes.
Abstract: We define an ensemble of lattices, and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings, sphere coverings, additive white Gaussian noise (AWGN) channel codes and mean-squared error (MSE) quantization codes. These lattices are generated by applying Construction A to a random linear code over a prime field of growing size, i.e., by "lifting" the code to /spl Ropf//sup n/.

460 citations

Journal ArticleDOI
Ram Zamir1, K. Feder1
27 Jun 1994
TL;DR: In entropy-coded dithered quantization, which can be modeled accurately as passing the source through an additive noise channel, this limit behavior implies that for large lattice dimension both the error and the bit rate approach theerror and the information rate of an additive white Gaussian noise (AWGN) channel.
Abstract: We present several results regarding the properties of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. We find that for the optimal lattice quantizers this noise is wide-sense-stationary and white. Any desirable noise spectra may be realized by an appropriate linear transformation ("shaping") of a lattice quantizer. As the dimension increases, the normalized second moment of the optimal lattice quantizer goes to 1/2/spl pi/e, and consequently the quantization noise approaches a white Gaussian process in the divergence sense. In entropy-coded dithered quantization, which can be modeled accurately as passing the source through an additive noise channel, this limit behavior implies that for large lattice dimension both the error and the bit rate approach the error and the information rate of an additive white Gaussian noise (AWGN) channel.

380 citations


Cited by
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[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Book
01 Jan 2005

9,038 citations

Proceedings Article
01 Jan 1991
TL;DR: It is concluded that properly augmented and power-controlled multiple-cell CDMA (code division multiple access) promises a quantum increase in current cellular capacity.
Abstract: It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

2,951 citations

Book
24 Oct 2001
TL;DR: Digital Watermarking covers the crucial research findings in the field and explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied.
Abstract: Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

2,849 citations

Journal ArticleDOI
TL;DR: Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR), and some numerical results are provided for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.
Abstract: A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j

2,616 citations