[Show abstract][Hide abstract] ABSTRACT: In Costa's dirty-paper channel, Gaussian random binning is able to eliminate the effect of interference which is known at the transmitter, and thus achieve capacity. We examine a generalization of the dirty-paper problem to a multiple access channel (MAC) setup, where structured (lattice-based) binning seems to be necessary to achieve capacity. In the dirty-MAC, two additive interference signals are present, one known to each transmitter but none to the receiver. The achievable rates using Costa's Gaussian binning vanish if both interference signals are strong. In contrast, it is shown that lattice-strategies (“lattice precoding”) can achieve positive rates, independent of the interference power. Furthermore, in some cases-which depend on the noise variance and power constraints-high-dimensional lattice strategies are in fact optimal. In particular, they are optimal in the limit of high SNR-where the capacity region of the dirty MAC with strong interference approaches that of a clean MAC whose power is governed by the minimum of the users' powers rather than their sum. The rate gap at high SNR between lattice-strategies and optimum (rather than Gaussian) random binning is conjectured to be <sup>1</sup>/<sub>2</sub> log<sub>2</sub>(π e /6) ≈ 0.254 bit. Thus, the doubly dirty MAC is another instance of a network setting, like the Körner-Marton problem, where (linear) structured coding is potentially better than random binning.
IEEE Transactions on Information Theory 09/2011; 57(8-57):5006 - 5035. DOI:10.1109/TIT.2011.2158883 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The general two-user memoryless multiple-access channel, with common channel state information known to the encoders, has no single-letter solution which explicitly characterizes its capacity region. In this paper a binary “dirty” multiple-access channel (MAC) with “common interference”, when the interference sequence is known to both encoders, is considered. We determine its sum-capacity, which equals to the capacity when full-cooperation between transmitters is allowed, contrary to the Gaussian case. We further derive an achievable rate region for this channel, by adopting the “onion-peeling” strategies which achieve the capacity region of the “clean” binary MAC. We show that the gap between the capacity region of the clean MAC and the achievable rate region of dirty MAC stems from the loss of the point-to-point binary dirty channel relative to the corresponding clean channel.
[Show abstract][Hide abstract] ABSTRACT: The general two-user memoryless multiple-access channel with partial or full channel state information among the encoders has no single-letter solution which explicitly characterizes its capacity region. In this paper a binary dirty multiple-access channel with interference known at one/both encoders is considered. Specifically, we derive formulas for the capacity region of the doubly-dirty multiple-access channel where each encoder knows one of two independent interference sequences and for the binary dirty multiple-access channel with a single informed user where the interference is known to only one encoder.
Information Theory Workshop, 2009. ITW 2009. IEEE; 11/2009
[Show abstract][Hide abstract] ABSTRACT: A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.
[Show abstract][Hide abstract] ABSTRACT: In this paper we provide an achievable rate region for the discrete memoryless multiple access channel with correlated state information known non-causally at the encoders using a random binning technique. This result is a generalization of the random binning technique used by Gel'fand and Pinsker for the problem with non-causal channel state information at the encoder in point to point communication.
[Show abstract][Hide abstract] ABSTRACT: For general memoryless systems, the typical information theoretic solution, when exists, has a ldquosingle-letterrdquo form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some single-letter distribution. Is that the form of the solution of any (information theoretic) problem? In fact, some counter examples are known, perhaps the most famous being the Korner-Marton ldquotwo help onerdquo problem, where the modulo-two sum of two binary sources is to be decoded from their independent encodings. In this paper we provide another counter example, the ldquodoubly-dirtyrdquo multiple access channel (MAC). Like the Korner-Marton problem, this example is associated with a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference but the receiver is not aware of any part of it. We give an explicit solution for the capacity region of a binary version of the doubly-dirty MAC, demonstrate how this capacity region can be approached using a linear coding scheme, and prove that the ldquobest known single-letter regionrdquo is strictly contained in it. We also state a conjecture regarding a similar rate loss of single letter characterization in the Gaussian case.
Information Theory Workshop, 2008. ITW '08. IEEE; 06/2008
[Show abstract][Hide abstract] ABSTRACT: For general memoryless systems, the typical information theoretic solution - when exists - has a "single-letter" form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some single-letter distribution. Is that the form of the solution of any (information theoretic) problem? In fact, some counter examples are known. The most famous is the "two help one" problem: Korner and Marton showed that if we want to decode the modulo-two sum of two binary sources from their independent encodings, then linear coding is better than random coding. In this paper we provide another counter example, the "doubly-dirty" multiple access channel (MAC). Like the Korner-Marton problem, this is a multi-terminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference but the receiver is not aware of any part of it. We give an explicit solution for the capacity region of a binary version of the doubly-dirty MAC, demonstrate how the capacity region can be approached using a linear coding scheme, and prove that the "best known single-letter region" is strictly contained in it. We also state a conjecture regarding a similar rate loss of single letter characterization in the Gaussian case.
IEEE Transactions on Information Theory 04/2008; 55(6). DOI:10.1109/TIT.2009.2018174 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study two generalizations of the writing on dirty paper problem. The first scenario is the cross interference multiple access channel, where each user knows the interference that accompanies the transmission of the other user. In the second scenario we consider a two-user multiple access chancel with a common interference known to both transmitters. For the first scenario, we provide new inner and outer bounds for the capacity region. While the capacity region for the second problem was previously known, we provide a constructive coding scheme which attains it.
[Show abstract][Hide abstract] ABSTRACT: We investigate the capacity loss for using uncorrelated Gaussian input over a multiple-input multiple-output (MIMO) linear additive-noise channel. We upper-bound the capacity loss by a universal constant C* which is independent of the channel matrix and the noise distribution. For a single-user MIMO channel with n<sub>t</sub> inputs and n<sub>r</sub> outputs C* = min [ 1/2, n<sub>r</sub>/n<sub>t</sub> log<sub>2</sub> (1+n<sub>t</sub>/n<sub>r</sub>) ] bit per input dimension (or 2C* bit per transmit antenna per second per hertz), under both total and per-input power constraints. If we restrict attention to (colored) Gaussian noise, then the capacity loss is upper-bounded by a smaller constant C<sub>G</sub> = n<sub>r</sub>/2n<sub>r</sub> log<sub>2</sub> (n<sub>t</sub>/n<sub>r</sub>) for n<sub>r</sub> ges n<sub>t</sub>/e, and C<sub>G</sub> = 0.265 otherwise, and this bound is tight for certain cases of channel matrix and noise covariance. We also derive similar bounds for the sum-capacity loss in multiuser MIMO channels. This includes in particular uncorrelated Gaussian transmission in a MIMO multiple-access channel (MAC), and "flat" Gaussian dirty-paper coding (DPC) in a MIMO broadcast channel. In the context of wireless communication, our results imply that the benefit of beamforming and spatial water-filling over simple isotropic transmission is limited. Moreover, the excess capacity of a point-to-point MIMO channel over the same MIMO channel in a multiuser configuration is bounded by a universal constant.
IEEE Transactions on Information Theory 12/2007; 53(11-53):3904 - 3920. DOI:10.1109/TIT.2007.907512 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the sum-capacity loss for using uncorrelated Gaussian inputs over multiple-input multiple-output (MIMO) power-constrained linear additive-noise channels in multi-user configurations. We show that the sum-capacity loss is bounded by a universal constant which depends only on the total number of input and output dimensions of the channel, but is independent of the channel matrix, the noise distribution and the number of users. Specifically, for a multiple-access channel with a total number of n<sub>t</sub> transmit antennas and base-station with n<sub>r</sub> receive antennas, the sum-capacity loss is at most C* = min{1/2, n<sub>r</sub>/2n<sub>t </sub> log<sub>2</sub>(1 + n<sub>t</sub>/n<sub>r</sub>)} bit per input dimension (or 1 bit per transmit antenna per second per Hertz). If we restrict attention to Gaussian noises, then the capacity loss is upper bounded by C<sub>G</sub>* = min{0.265, 0.265n<sub>r</sub>/n<sub>t</sub> log<sub>2</sub>(n<sub>t</sub>/n<sub>r</sub>)}, and this bound is tight for certain channel matrices and noise spectra. We show also that the same bounds hold for the sum-capacity loss of uncorrelated Gaussian input over linear MIMO broadcast channels, input distribution being interpreted either in terms of the equivalent point-to-point channel with Sato condition, or as the output distribution of a "dirty-paper" transmitter. One implication of these results is the limited value of coherence and water-filling in spatial transmission. Another implication is the limited capacity loss in multi-user configurations relative to the fully cooperative (point-to-point) channel
Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on; 10/2005
[Show abstract][Hide abstract] ABSTRACT: We investigate the capacity loss of an uncorrelated Gaussian input with equal power (i.i.d. Gaussian input) over a multi-input multi-output linear additive noise (not necessarily Gaussian nor memoryless) channel. Previous work showed that this input is the best input in the case of Gaussian noise, assuming the channel matrix is known at the receiver but unknown at the transmitter. We show that i.i.d. Gaussian is a robust input also when the noise is not Gaussian. Specifically, we show that for n<sub>t</sub> transmit antennas and n<sub>r</sub> receive antennas, the capacity loss of an i.i.d. Gaussian input is smaller than min{n<sub>t</sub>/2, (n<sub>r</sub>/2)log<sub>2</sub>(1 + n<sub>t</sub>/n<sub>r</sub>)} bits, for any noise and channel matrix. This bound is apparently not tight. Nevertheless, for the case of Gaussian noise we derive a stronger bound which is tight for a "critical" channel matrix: (n<sub>r</sub>/2)log<sub>2</sub>(n<sub>t</sub>/n<sub>r</sub>) bits for 1≤ n<sub>r</sub>≤(n<sub>t</sub>/e) and (n<sub>t</sub>/2)(log<sub>2</sub>(e))/e bits for n<sub>r</sub>≥(n<sub>t</sub>/e).
Electrical and Electronics Engineers in Israel, 2004. Proceedings. 2004 23rd IEEE Convention of; 10/2004
[Show abstract][Hide abstract] ABSTRACT: We consider multi dimensional dirty paper coding at low SNR, and propose a low rate precoding scheme which combines MMSE estimation, dithering and a variant of nested codes, based on concatenation of a "syndrome dilution" code and a "syndrome-to-coset" modulation code.
Information Theory, 2003. Proceedings. IEEE International Symposium on; 01/2003
[Show abstract][Hide abstract] ABSTRACT: We investigate the application of the nested coding framework for cancelling known interference at low SNR, that is P<sub>X</sub>/P<sub>Z</sub>≈1 and below. We consider multi-dimensional precoding, with anticipation of N<sub>s</sub>>1 "future" interference samples. Unlike non-precoded transmission, where capacity can be achieved at low SNR without shaping, optimum precoding at low SNR does require shaping. Eyuboglu and Forney's trellis precoding scheme combines Tomlinson-Harashima precoding and trellis shaping, to achieve both coding and shaping gains in transmission over intersymbol interference channel with Euclidean distance decoder. However, the standard configuration of this scheme does not support precoding at low SNR, where the capacity is less than 1bit/dim. Inspired by the nested lattices approach, we propose a variant of trellis precoding which combines MMSE estimation, dithering and construction of nested lattices which approach the interference channel capacity at low SNR.
Electrical and Electronics Engineers in Israel, 2002. The 22nd Convention of; 01/2003