Non white Gaussian multiple access channels with feedback

Although feedback does not increase the capacity of an additive white noise Gaussian channel, it enables prediction of the noise for non-white additive Gaussian noise channels and results in an improvement of capacity, but at most by a factor of 2 (Pinsker, Ebert, Pombra, and Cover). Although the capacity of white noise channels cannot be increased by feedback, multiple access white noise channels have a capacity increase due to the cooperation induced by feedback. Thomas has shown that the total capacity (sum of the rates of all the senders) of an m-user Gaussian white noise multiple access channel with feedback is less than twice the total capacity without feedback. The present authors show that this factor of 2 bound holds even when cooperation and prediction are combined, by proving that feedback increases the total capacity of an m-user multiple access channel with non-white additive Gaussian noise by at most a factor of 2     

Mutual information of the white Gaussian channel with and without feedback

The following model for the white Gaussian channel with or without feedback is considered: begin{equation} Y(t) = int_o ^{t} phi (s, Y_o ^{s} ,m) ds + W(t) end{equation} wheremdenotes the message,Y(t)denotes the channel output at timet,Y_o ^ {t}denotes the sample pathY(theta), 0 leq theta leq t. W(t)is the Brownian motion representing noise, andphi(s, y_o ^ {s} ,m)is the channel input (modulator output). It is shown that, under some general assumptions, the amount of mutual informationI(Y_o ^{T} ,m)between the messagemand the output pathY_o ^ {T}is directly related to the mean-square causal filtering error of estimatingphi (t, Y_o ^{t} ,m)from the received dataY_o ^{T} , 0 leq t leq T. It follows, as a corollary to the result forI(Y_o ^ {T} ,m), that feedback can not increase the capacity of the nonband-limited additive white Gaussian noise channel.     

An achievable rate region and a capacity outer bound for 3‐user Gaussian multiple access channel with feedback

Extension of the Ozarow capacity theorem for 2‐transmitter Gaussian multiple access channel (MAC) with feedback to the channels with more than 2 transmitters is a widely studied and long standing problem (for example, see the Kramer sum‐capacity region). In this paper, we investigate and analyze this possible extension. Specifically, exploiting a class of Schalkwijk‐Kailath linear feedback codes, we obtain an achievable rate region for 3‐user Gaussian MAC with full feedback and also a capacity outer bound. Then the results are extended for a case where there is no feedback link for one user, and the corresponding achievable rate region and capacity outer bound are computed. Furthermore, the gap between the derived rates and the sum capacity of 3‐user Gaussian MAC with full and partial feedback is computed under special assumptions.     

Feedback can at most double Gaussian multiple access channel capacity (Corresp.)

The converse for the discrete memoryless multiple access channel is generalized and is used to derive strong bounds on the total capacity (sum of the rates of all the senders) of anm-user Gaussian multiple access channel in terms of the input covariance matrix. These bounds are used to show that the total capacity of the channel with feedback is less than twice the total capacity without feedback. The converse for the general multiple access channel is also used to show that for anym-user multiple access channel, feedback cannot increase the total capacity by more than a factor ofm.     

The capacity of the physically degraded Gaussian broadcast channel with feedback (Corresp.)

Bounds on the output entropy of the additive white Gaussian noise (AWGN) channel with feedback are used to prove that the capacity of the degraded additive white Gaussian noise (DAWGN) broadcast channel is not increased by feedback.     

Gaussian feedback capacity

The capacity of time-varying additive Gaussian noise channels with feedback is characterized. Toward this end, an asymptotic equipartition theorem for nonstationary Gaussian processes is proved. Then, with the aid of certain matrix inequalities, it is proved that the feedback capacity C_FB in bits per transmission and the nonfeedback capacity C satisfy C⩽C_FB ⩽2C and C⩽C_FB⩽ C+1/2     

Allocation of resources for the Gaussian multiple access channel with practical partial cooperation

A Gaussian multiple access channel, with partial cooperation between sources, is considered. We develop an encoding scheme in which the transmission is carried out over three orthogonal time phases. The first two phases are exploited such that the two sources can practically and partially exchange their messages. In particular, each phase is terminated when each user can generate the other user’s codeword. Then, the two users can cooperatively transmit in the third phase. This formulation is used to (i) develop the achievable rate region, and (ii) numerically study the importance of each phase’s length and the allocated power to each user in the three characterized transmission phases.     

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.     

An upper bound to the capacity of the band-limited Gaussian autoregressive channel with noiseless feedback

Upper bounds to the capacity of band-limited Gaussianmth-order autoregressive channels with feedback and average energy constraintEare derived. These are the only known hounds on one- and two-way autoregressive channels of order greater than one. They are the tightest known for the first-order case. In this case letalpha_1be the regression coefficient,sigma^2the innovation variance,Nthe number of channel iterations per source symbol, ande = E/N; then the first-order capacityC^1is bounded by begin{equation} C^1 leq begin{cases} frac{1}{2} ln [frac{e}{sigma^2}(1+ mid alpha_1 mid ) ^ 2 +1], & frac{e}{sigma^2} leq frac{1}{1- alpha_1^2} \ frac{1}{2} ln [frac{e}{sigma^2} + frac{2mid alpha_1 mid}{sqrt{1-alpha_1^2}} sqrt{frac{e}{simga^2}} + frac{1}{1-alpha_1^2}], & text{elsewhere}.\ end{cases} end{equation} This is equal to capacity without feedback for very low and very highe/sigma^2and is less than twice this one-way capacity everywhere.     

On Gaussian feedback capacity

M. Pinsker and P. Ebert (Bell Syst. Tech. J., p.1705-1712, Oct.1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Recently, T. Cover and S. Pombra (ibid., vol.35, no.1, p.37-43, Jan.1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by L.H. Ozarow (to appear in IEEE Trans. Inf. Theory) using a different bounding technique     

Packet multiple access for channel with binary feedback, capture, and multiple reception

This paper considers the multiple access of mobile users to a common wireless channel. The channel is slotted and the binary feedback (empty slot/nonempty slot) is sent to all accessing users. If a slot was not empty and only one user transmitted in it, the transmission is considered successful. Only the user, which had the successful transmission, receives information about its success. In the Introduction, the paper gives a review of known multiple-access algorithms for such a channel. Then our algorithm is constructed that has none of the weaknesses of the algorithms discussed in the Introduction. The algorithm is stable, in contrast to the ALOHA algorithm. It can work in a channel with capture and multiple reception. Without them, the algorithm has a throughput of 0.2891. It is shown how capture and multiple reception can increase the algorithm throughput to 0.6548 and decrease the packet delay for some fading models. The average packet delay and variance are found for two fading models. The models are Rayleigh fading with incoherent and coherent combining of joint interference power. The accessing traffic is Poisson.     

Partial feedback for the discrete memoryless multiple access channel (Corresp.)

The region Cover and Leung found for the discrete memoryless multiple access channel with feedback to both encoders is proved achievable also with feedback to only one encoder. The novel ideas of nonrandom partitions and restricted decoding are used to avoid list coding techniques.     

Near capacity multiple access scheme for interference channel usingcomplex-valued signals

A multiuser detection scheme is proposed for channels using non-spread signals. Trellis encoders and different random interleavers are employed for each user to remove the ambiguity in decoding each user's data from the composite received signal. With symbol-by-symbol soft decision, near channel capacity performance is obtained     

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     

The convex-concave characteristics of Gaussian channel capacity functions

In this correspondence, we give several inherent properties of the capacity function of a Gaussian channel with and without feedback by using some operator inequalities and matrix analysis. We give a new proof method which is different from the method appearing in: K. Yanagi and H. W. Chen, "Operator inequality and its application to information theory," Taiwanese J. Math., vol. 4, no. 3, pp. 407-416, Sep. 2000. We obtain the following results: C/sub n,Z/(P) and C/sub n,FB,Z/(P) are both concave functions of P, C/sub n,Z/(P) is a convex function of the noise covariance matrix and C/sub n,FB,Z/(P) is a convex-like function of the noise covariance matrix. This new proof method is very elementary and the results shall help study the capacity of Gaussian channel. Finally, we state a conjecture concerning the convexity of C/sub n,FB,/spl middot//(P).     

Optimal coding in two-user white Gaussian channels with feedback

The optimal coding problem in two-user white Gaussian channels with feedback is discussed. The messages are taken as Gauss-Markov processes. The optimal decoder pair and the optimal linear encoder pair are developed. A nonlinear class (additive feedback type) of encoder pairs in which the optimal linear encooer pair is optimal is presented.     

Information capacity of the stationary Gaussian channel

The averaged information capacity of the mismatched stationary continuous-time Gaussian channel is considered, in the limit as the observation time becomes infinite. It is required only that the signal satisfy a reproducing kernel Hilbert space constraint on expected energy. This requires the, signal energy to be distributed in regions where the noise energy, is not too small, and is the weakest condition that provides finite capacity. In the case when both the noise covariance and the filter on the message are expressed by rational functions, the results complement those previously obtained by Gallager and Holsinger (1968), and the combination gives a complete solution to the capacity problem. The treatment provides a desirable generality on the class of transmitted signals that is not present in previous treatments     

On the converse to the coding theorem for the continuous time white Gaussian channel with feedback (Corresp.)

A converse to the coding theorem for the continuous time white Gaussian channel with feedback is derived by reducing the continuous time codewords to discrete time codewords in a way that preserves their Causal property.     

Performance of multiple access channels with asymmetric feedback

Channel state feedback at the transmitter is extensively used to increase the reliability of wireless transmissions. In multiuser systems, the downlink capacity to different users is often different due to the near-far effect. We capture this asymmetry by introducing an asymmetric feedback model where different users get a different amount of feedback from the base station. First, we derive the outage probability for the optimum maximum-likelihood receiver which forms an upper bound on the diversity-multiplexing performance. This is accompanied by the conditions under which these bounds can be achieved. Second, we analyze the performance of two popular suboptimal receivers: the spatial decorrelator and the successive interference cancellation receiver. As a special case, when there is no asymmetry, the performance matches feedback-based single-user performance in many scenarios.     

Necessary and sufficient condition for capacity of the discretetime Gaussian channel to be increased by feedback

The problem of whether the capacity of a discrete-time Gaussian channel is increased by feedback or not is considered. It is well known that the capacity of a white Gaussian channel under an average power constraint is not changed by feedback. The necessary condition under which the capacity of a nonwhite Gaussian channel with blockwise white noise is increased by feedback is given