Outer bounds on the capacity of interference channels (Corresp.)

New outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and Gaussian interference channels. The bound for discrete channels coincides with the capacity region in special cases. The bound for Gaussian channels improves previous knowledge when the interference is of medium strength.     

Upper bounds on the capacity of Gaussian channels with feedback

The capacity of the discrete-time additive Gaussian channel without feedback is known. A class of upper bounds on the capacity with noiseless feedback that are quite good for some exemplary channels is obtained     

Upper bounds on capacity for a constrained Gaussian channel

A low-pass and a bandpass additive white Gaussian noise channel with a peak-power constraint imposed on otherwise arbitrary input signals are considered. Upper bounds on the capacity of such channels are derived. They are strictly less than the capacity of the channel when the peak-power constrain is removed and replaced by the average-power constraint, for which the Gaussian inputs are optimum. This provides the answer to an often-posed question: peak-power limiting in the case of bandlimited channels does reduce capacity, whereas in infinite bandwidth channels it does not, as is well known. For an ideal low-pass filter of bandwidth B, the upper bound is Blog 0.934P/(N₀B) for P/( N₀B)≫1, where P is the peak power of the input signal and N₀/2 is the double-sided power spectral density of the additive white Gaussian noise     

Lower bounds in the capacity of permutation channels

In this paper, permutation channels, which include the rank channels and doubly uniform channels, are defined. A lower bound on the capacities of these channels is obtained with help of nonparametric signal-detection theory. This bound reduces to the actual capacity for memoryless doubly uniform channels by properly selecting the associated nonparametric detectors, The lower bounds on the capacities of the rank channels are expressed in terms of Kendalrs rank correlation coefficient. When the signal power is low, the comparison between a rank channel and a memoryless binary symmetric channel is expressed in terms of the Pitman-Noether asymptotic relative efficiency.     

Sum capacity of Gaussian vector broadcast channels

This paper characterizes the sum capacity of a class of potentially nondegraded Gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers. Coordination is allowed among the transmit terminals, but not among the receive terminals. The sum capacity is shown to be a saddle-point of a Gaussian mutual information game, where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information. The sum capacity is achieved using a precoding strategy for Gaussian channels with additive side information noncausally known at the transmitter. The optimal precoding structure is shown to correspond to a decision-feedback equalizer that decomposes the broadcast channel into a series of single-user channels with interference pre-subtracted at the transmitter.     

Exponential error bounds for random codes on Gaussian arbitrarily varying channels

The main objective is to develop exponential bounds to the best error probability achievable with random coding on the Gaussian arbitrarily varying channel (GAVC) in the one case where a (strong) capacity exists (i.e., with peak time-averaged power constraints on both the transmitter and interference). The GAVC models a channel corrupted by thermal noise and by an unknown interfering signal of bounded power. The upper and lower bounds to the best error probability achievable on this channel with random coding are presented. The asymptotic exponents of these bounds agree in a range of rates near capacity. The exponents are universally larger than the corresponding exponents for the discrete-time Gaussian channel with the same capacity. It is further shown that the decoder can be taken to be the minimum Euclidean distance rule at all rates less than capacity.<>     

On the capacity of channels with unknown interference

The process of communicating in the presence of interference that is unknown or hostile is modeled as a two-person zero-sum game with the communicator and the jammer as the players. The objective function considered is the rate of reliable communication. The communicator's strategies are encoders and distributions on a set of quantizers. The jammer's strategies are distributions on the noise power subject to certain constraints. Various conditions are considered on the jammer's strategy set and on the communicator's knowledge. For the case where the decoder is uninformed of the actual quantizer chosen, it is shown that, from the communicator's perspective, the worst-case jamming strategy is a distribution concentrated on a finite number of points, thereby converting a functional optimization problem into a nonlinear programming problem. Moreover, the worst-case distributions can be characterized by means of necessary and sufficient conditions which are easy to verify. For the case where the decoder is informed of the actual quantizer chosen, the existence of saddle-point strategies is demonstrated. The analysis is also seen to be valid for a number of situations where the jammer is adaptive     

On the asymptotic capacity of stationary Gaussian fading channels

We consider a peak-power-limited single-antenna flat complex-Gaussian fading channel where the receiver and transmitter, while fully cognizant of the distribution of the fading process, have no knowledge of its realization. Upper and lower bounds on channel capacity are derived, with special emphasis on tightness in the high signal-to-noise ratio (SNR) regime. Necessary and sufficient conditions (in terms of the autocorrelation of the fading process) are derived for capacity to grow double-logarithmically in the SNR. For cases in which capacity increases logarithmically in the SNR, we provide an expression for the "pre-log", i.e., for the asymptotic ratio between channel capacity and the logarithm of the SNR. This ratio is given by the Lebesgue measure of the set of harmonics where the spectral density of the fading process is zero. We finally demonstrate that the asymptotic dependence of channel capacity on the SNR need not be limited to logarithmic or double-logarithmic behaviors. We exhibit power spectra for which capacity grows as a fractional power of the logarithm of the SNR     

The capacity of the Gaussian interference channel under strong interference (Corresp.)

The capacity region of a Gaussian interference channel with two separate messages is obtained for the case of moderately strong interference. It is shown that the region coincides with the one where both messages are required in both receiving terminals.     

FDMA capacity of Gaussian multiple-access channels with ISI

This paper proposes a numerical method for characterizing the rate region achievable with frequency-division multiple access (FDMA) for a Gaussian multiple-access channel with intersymbol interference. The frequency spectrum is divided into discrete frequency bins and the discrete bin-assignment problem is shown to have a convex relaxation, making it tractable to numerical optimization algorithms. A practical low-complexity algorithm for the two-user case is also proposed. The algorithm is based on the observation that the optimal frequency partition has a two-band structure when the two channels are identical or when the signal-to-noise ratio is high. The simulation result shows that the algorithm performs well in other cases as well. The FDMA-capacity algorithm is used to devise the optimal frequency-division duplex plan for very-high-speed digital subscriber lines     

New outer bounds to capacity regions of two-way channels

Shannon's two-way channel problem has attracted the attention of information theorists for many years. In a classic paper Shannon gave both an outer and an inner bound to the capacity region of the two-way channel. Schalkwijk recently obtained an improvement to the inner bound for the Blackwell multiplying channel (BMC). We present the first improvements on Shannon's outer bound. Calculation shows that our results are close to optimum when applied to the BMC.     

On the capacity of binary and Gaussian channels withrun-length-limited inputs

Bounds on the capacity of binary symmetric channels and additive Gaussian channels with run-length-limited two-level (binary, bipolar) inputs are presented, and their tightness is demonstrated for some cases. Stationary input sequences, which do not degrade capacity, are considered when deriving the bounds. Lower bounds on the magnetic recording density for a simple continuous-time recording model incorporating a minimal intertransition constraint are evaluated for soft and hard decisions. A superiority of about 1.5 dB in signal-to-noise ratio is observed for the soft-decision scheme     

Universal decoding for memoryless Gaussian channels with adeterministic interference

A universal decoding procedure is proposed for memoryless Gaussian channels with deterministic interfering signals from a certain class. The proposed decoder is universal in the sense that it is independent of the channel parameters and the unknown interfering signal, and, at the same time, attains the same random coding error exponent as the optimal maximum likelihood (ML) decoder, which utilizes full knowledge of the channel parameters and the interfering signal. The proposed decoding rule can be regarded as a continuous-alphabet version of the universal maximum mutual information decoder     

The intersymbol interference channel: lower bounds on capacity andchannel precoding loss

The discrete-time additive Gaussian intersymbol interference (ISI) channel with i.i.d. (not necessarily Gaussian) input signals is considered. Several new and old lower bounds on the capacity are derived in a unified manner by assuming different front-end receiver filters, in particular the sampled whitened matched filter (SWMF) and the minimum mean-squared error-decision feedback equalizer (MMSE-DFE) filter. The features of the bounds are demonstrated and compared in several examples with binary and quaternary input signals. It is also shown that the effect of an ideal post-cursor or tail cancellation, in an information-preserving context, depends primarily on the front-end filter. While, as is well known, ideal post-cursor cancellation at the output of the SWMF decreases the information, the opposite trend is seen when an MMSE-DFE front filter is considered. This observation reflects the basic theoretical obstacles in precoding, i.e., ideal post-cursor cancellation in the presence of a pre-cursor. It is used to assess the inherent loss (in terms of information rates as compared to the rates achievable with the hypothetical ideal post-cursor cancellation) associated with any post-cursor cancellation technique such as precoding, DFE, or other variants, when operating in synergy with the MMSE-DFE front-end filter. The effect of the front-end filter on an ideally interleaved, precoded coded-modulation system is also addressed     

On the transport capacity of Gaussian multiple access and broadcast channels

We study the transport capacity of the Gaussian multiple access channel (MAC), which consists of multiple transmitters and a single receiver, and the Gaussian broadcast channel (BC), which consists of a single transmitter and multiple receivers. The transport capacity is defined as the sum, over all transmitters (for the MAC) or receivers (for the BC), of the product of the data rate with a reward r(x) which is a function of the distance x that the data travels. In the case of the MAC, assuming that the sum of the transmit powers is upper bounded, we calculate in closed form the optimal power allocation among the transmitters, that maximizes the transport capacity, using Karush-Kuhn-Tucker (KKT) conditions. We also derive asymptotic expressions for the optimal power allocation, that hold as the number of transmitters approaches infinity, using the most-rapid-approach method of the calculus of variations. In the case of the BC, we calculate in closed form the optimal allocation of the transmit power among the signals to the different receivers, both for a finite number of receivers and for the case of asymptotically many receivers, using our results for the MAC together with duality arguments. Our results can be used to gain intuition and develop good design principles in a variety of settings. For example, they apply to the uplink and downlink channel of cellular networks, and also to sensor networks which consist of multiple sensors that communicate with a single central station. Work was carried out while all authors were with the Telecommunications Research Center Vienna (ftw.), and supported by K plus funding for the ftw. project I0 “Signal and Information Processing.” Parts of this work have appeared, in preliminary form, in [1,2,3], Gautam A. Gupta holds a joint B.S./M.S. degree in mathematics and computing at the Department of Mathematics of the Indian Institute of Technology at New Delhi. During the summer of 2003, he attended a summer course on Probability and Statistical Mechanics organized by the Scoula Normale Superiore, in Pisa, Italy. During the summers of 2004 and 2005 he worked at the Telecommunications Research Center Vienna (ftw.) as a summer intern. During the spring of 2006, he was a visitor at the Norwegian University of Science and Technology, working toward his M. S. Thesis. Stavros Toumpis received the Diploma in electrical and computer engineering from the National Technical University of Athens, Greece, in 1997, the M.S. degrees in electrical engineering and mathematics from Stanford University, CA, in 1999 and 2002, respectively, and the Ph.D. degree in electrical engineering, also from Stanford, in 2003. From 1998 to 1999, he worked as a Research Assistant for the Mars Global Surveyor Radio Science Team, providing operational support. From 2000 to 2003, he was a Member of the Wireless Systems Laboratory, at Stanford University. From 2003 to 2005, he was a Senior Researcher with the Telecommunications Research Center Vienna (ftw.), in Vienna, Austria. Since 2005, he is a Lecturer at the Department of Electrical and Computer Engineering of the University of Cyprus. His research is on wireless ad hoc networks, with emphasis on their capacity, the effects of mobility on their performance, medium access control, and information theoretic issues. Jossy Sayir received his Dipl. El.-Ing. degree from the ETH Zurich in 1991. From 1991 to 1993, he worked as a development engineer for Motorola Communications in Tel Aviv, Israel, contributing to the design of the first digital mobile radio system ever produced by Motorola. He returned to ETH from 1993 to 1999, getting his PhD in 1999 under the supervision of Prof. J.L. Massey. The title of his thesis is “On Coding by Probability Transformation.” Since 2000, he has been employed at the Telecommunications Research Center (ftw) in Vienna, Austria, as a senior researcher. His research interests include iterative decoding methods, joint source and channel coding, numerical capacity computation algorithms, Markov sources, and wireless ad hoc and sensor networks. Since July 2002, he manages part of the strategic research activities at Ftw and supervises a group of researchers. He has taught courses on Turbo and related codes at Vienna University of Technology and at the University of Aalborg, Denmark. He has served on the organization committees of several international conferences and workshops. Ralf R. Müller was born in Schwabach, Germany, 1970. He received the Dipl.-Ing. and Dr.Ing. degree with distinction from University of Erlangen-Nuremberg in 1996 and 1999, respectively. From 2000 to 2004, he was with Forschungszentrum Telekommunikation Wien (Vienna Telecommunications Research Center) in Vienna, Austria. Since 2005 he has been a full professor at the Department of Electronics and Telecommunications at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway. He held visiting appointments at Princeton University, U.S.A., Institute Eurecom, France, The University of Melbourne, Australia, and The National University of Singapore and was an adjunct professor at Vienna University of Technology. Dr. Müller received the Leonard G. Abraham Prize (jointly with Sergio S. Verdú) from the IEEE Communications Society and the Johann-Philipp-Reis Prize (jointly with Robert Fischer). He was also presented an award by the Vodafone Foundation for Mobile Communications and two more awards from the German Information Technology Society (ITG). Dr. Müller is currently serving as an associate editor for the IEEE Transactions on Information Theory.     

Channel capacity and state estimation for state-dependent Gaussian channels

We formulate a problem of state information transmission over a state-dependent channel with states known at the transmitter. In particular, we solve a problem of minimizing the mean-squared channel state estimation error E/spl par/S/sup n/ - S/spl circ//sup n//spl par/ for a state-dependent additive Gaussian channel Y/sup n/ = X/sup n/ + S/sup n/ + Z/sup n/ with an independent and identically distributed (i.i.d.) Gaussian state sequence S/sup n/ = (S/sub 1/, ..., S/sub n/) known at the transmitter and an unknown i.i.d. additive Gaussian noise Z/sup n/. We show that a simple technique of direct state amplification (i.e., X/sup n/ = /spl alpha/S/sup n/), where the transmitter uses its entire power budget to amplify the channel state, yields the minimum mean-squared state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. We characterize the optimal tradeoff between the rate R of the independent information that can be reliably transmitted and the mean-squared state estimation error D. We show that any optimal (R, D) tradeoff pair can be achieved via a simple power-sharing technique, whereby the transmitter power is appropriately allocated between pure information transmission and state amplification.     

The coding capacity of mismatched Gaussian channels (Corresp.)

Bounds on the coding capacity of Gaussian channels are obtained when the power constraint on the signal is mismatched to the channel noise. In the case of some feedback channels in which the noise has a Cramér-Hida representation of finite multiplicity, an exact expression for the coding capacity is given.     

Gaussian multiaccess channels with ISI: capacity region andmultiuser water-filling

The capacity region of a two-user Gaussian multiaccess channel with intersymbol interference (ISI) in which the inputs pass through respective linear systems and are superimposed before being corrupted by an additive Gaussian noise process is discussed. A geometrical method for obtaining the optimal input power spectral densities and the capacity region is presented. This method can be viewed as a nontrivial generalization of the single-user water-filling argument. It is shown that, as in the traditional memoryless multiaccess channel, frequency-division multiaccess (FDMA) with optimally selected frequency bands for each user achieves the total capacity of the multiuser Gaussian multiaccess channel with ISI. However, the capacity region of the two-user channel with memory is, in general, not a pentagon unless the channel transfer functions for both users are identical     

Symmetric capacity and signal design for L-out-of-Ksymbol-synchronous CDMA Gaussian channels

We consider the symbol-synchronous Gaussian L-out-of-K code-division multiaccess channel, and obtain the capacity region and the upper and lower bounds to the symmetric capacity. The capacity region is found to be the same with or without frame synchronism. The lower bound depends on the signature waveforms through the eigenvalues of the SNR-weighted crosscorrelation matrix. We find a sufficient condition for the signature waveform set to maximize this lower bound and give an algorithm to construct a set of signature waveforms satisfying the sufficient condition