This paper presents a stochastic geometry model for studying spatiotemporal base station cooperation in a cellular network. Unlike most previous related works in the literature, the paper focuses on the coverage probability at the typical cellcorner user, i.e., a user that is equidistant to its three neighboring base stations (BSs). Three schemes are considered: joint transmission, base station silencing, and the Alamouti space-time code. In addition, BSs are allowed to cooperatively retransmit data across consecutive time slots, such that the cell-corner user can benefit from time diversity. For all these schemes, an expression for the coverage probability at the cell-corner user is derived. The best performing scheme is shown to be the Alamouti code, when only two BSs cooperate. Otherwise, cooperative retransmission performs the best in the high-coverage regime, while joint transmission without retransmission outperforms the remaining schemes in all other regimes. These results extend previous findings on spatiotemporal base station cooperation that only applied to the typical user in a cellular network.

Several new expressions for the anytime capacity of Sahai and Mitter are presented for a time-varying rate-limited channel with noiseless output feedback. These follow from a parametric characterization obtained in the case of Markov channels, and include an explicit formula for the r-bit Markov erasure channel, as well as formulas for memoryless rate processes including Binomial, Poisson, and Geometric distributions. Beside the memoryless erasure channel and the additive white Gaussian noise channel with input power constraint, these are the only cases where explicit anytime capacity formulas are obtained. At the basis of these results is the study of the threshold function for mth moment stabilization of a scalar linear system controlled over a Markov time-varying digital feedback channel that depends on m and on the channel's parameters. This threshold is shown to be a continuous and strictly decreasing function of m and to have as extreme values the Shannon capacity and the zero-error capacity as m tends to zero and infinity, respectively. Its operational interpretation is that of achievable communication rate, subject to a reliability constraint.

This paper studies downlink communication in a heterogeneous cellular network where a set of geographically separated base stations (BSs) cooperates in transmitting data to a common receiver. If a decoding error occurs, data is cooperatively retransmitted by a possibly different set of BSs, such that the receiver can benefit from spatiotemporal BS cooperation. Specific cooperation techniques studied in this paper include joint transmission, base station silencing, and the Alamouti space-time code. Using tools from stochastic geometry, the coverage probability at the typical user is characterized as an integral function of the network parameters and the sets of cooperating BSs. The expressions derived reveal the existence of two qualitatively different operating regimes. In the high-coverage regime, the typical user is diversity-limited, so cooperation techniques exploiting spatiotemporal diversity are highly effective in increasing coverage. It is shown that retransmissions always yield time diversity, while channel state information at the transmitters is required to harvest spatial diversity via joint transmission. In the low-coverage regime, on the other hand, the typical user is interference-limited, so cooperation techniques such as joint transmission and base station silencing are effective in increasing coverage as they suppress part of the interference power.

Hybrid analog-digital coding has been used for several communication scenarios, such as joint source-channel coding of Gaussian sources over Gaussian channels and relay communication over Gaussian networks. In this paper, a generalized hybrid coding technique is proposed for communication over discrete memoryless and Gaussian systems, and its utility is demonstrated via three examples-lossy joint source-channel coding over multiple access channels, channel coding over two-way relay channels, and channel coding over diamond networks. The corresponding coding schemes recover and extend several existing results in the literature.

This paper studies spatiotemporal cooperation between base stations in the presence of interference in a heterogeneous cellular network. The focus of the paper is the cooperative retransmission scenario, where a set of randomly located base stations that are selected based on their average received powers, possibly belonging to different network tiers, jointly transmit data in each transmission. If a decoding error occurs in the first transmission, data is cooperatively retransmitted by a possibly different set of BSs, such that the receiver can benefit from spatiotemporal BS cooperation. Using tools from stochastic geometry, the coverage probability at the typical user is characterized as an integral function of the network parameters and the sets of cooperating BSs. An integral expression for the coverage probability is also derived for the case when the typical user is able to perform maximum ratio combining (MRC) of the received copies in two transmissions. Numerical evaluation shows that in the high coverage regime spatiotemporal cooperation outperforms joint transmission with no retransmissions and that the gains extend to all regimes if the user has MRC capability.

Motivated by the ongoing discussion on coordinated multipoint in wireless cellular standard bodies, this paper considers the problem of base station cooperation in the downlink of heterogeneous cellular networks. The focus of this paper is the joint transmission scenario, where an ideal backhaul network allows a set of randomly located base stations, possibly belonging to different network tiers, to jointly transmit data, to mitigate intercell interference and hence improve coverage and spectral efficiency. Using tools from stochastic geometry, an integral expression for the network coverage probability is derived in the scenario where the typical user located at an arbitrary location, i.e., the general user, receives data from a pool of base stations that are selected based on their average received power levels. An expression for the coverage probability is also derived for the typical user located at the point equidistant from three base stations, which we refer to as the worst case user. In the special case where cooperation is limited to two base stations, numerical evaluations illustrate absolute gains in coverage probability of up to 17% for the general user and 24% for the worst case user compared with the noncooperative case. It is also shown that no diversity gain is achieved using noncoherent joint transmission, whereas full diversity gain can be achieved at the receiver if the transmitting base stations have channel state information.

We consider the\(K\geq 2\)-user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk and Kailath’s scheme for point-to-point channels or Ozarow and Leung’s scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity\(C\)(which is the same with and without feedback). In the extreme case where the number of receivers\(K\to \infty \), the largest rate achieved by linear-feedback schemes with a message point tends to 0. To contrast this negative result, we describe a scheme for rate-limited feedback that uses the feedback in an intermittent way, i.e., the receivers send feedback signals only in few channel uses. This scheme achieves all rates\(R\)up to capacity\(C\)with an\(L\)th order exponential decay of the probability of error if the feedback rate\(R_{\text {fb}}\)is at least\((L-1)R\)for some positive integer\(L\).

The performance of cooperation strategies for broadcast services sharing a common wireless channel is studied in the framework of coalitional game theory. Two strategies are examined. The first represents an open sharing model where each service provider is allowed to transmit at any time but simultaneous transmissions result in interference. It is shown analytically that in the absence of coordination cost, the grand coalition formed by all providers cooperating to avoid simultaneous transmissions is both sum-rate optimal and stable. The second strategy represents an orthogonal access method where service providers are granted exclusive access to a subset of the available channels, each having a guaranteed successful transmission opportunity. In the absence of coordination cost, the grand coalition where all providers cooperate by sharing their guaranteed right to access the channel is sum-rate optimal but unstable, in the sense that some group of providers may have an incentive to deviate from the grand coalition. In the presence of coordination cost, a different scenario arises. In both models large coalitions do not form, and simulation results suggest that the open access model for large networks can lead to a regime where performance is considerably limited by interference.

We consider the problem of lossy communication of correlated sources over multiple access channels with noiseless causal feedback. A sufficient condition for lossy transmission is presented, which generalizes several previous results on communication over multiple access channels, recovering as special cases channel coding results by King, Cover, and Leung, and extending a previous sufficient condition for lossless communication by Cover, El Gamal, and Salehi. The proposed coding scheme is based on a recently developed analog-digital hybrid coding scheme for joint source-channel coding combined with block-Markov coding.

A code for communication over the k-receiver complex additive white Gaussian noise broadcast channel (BC) with feedback is presented and analyzed using tools from the theory of linear quadratic Gaussian optimal control. It is shown that the performance of this code depends on the noise correlation at the receivers and it is related to the solution of a discrete algebraic Riccati equation. For the case of independent noises, the sum rate achieved by the proposed code, satisfying average power constraint P, is characterized as 1/2 log(1+Pφ), where the coefficient φ ∈ [1,k] quantifies the power gain due to the presence of feedback. This includes a previous result by Elia and strictly improves upon the codes by Ozarow and Leung and by Kramer. When the noises are correlated, the prelog of the sum capacity of the BC with feedback can be strictly greater than 1. It is established that for all noise covariance matrices of rank r the prelog of the sum capacity is at most k-r+1 and, conversely, there exists a noise covariance matrix of rank r for which the proposed code achieves this upper bound. This generalizes a previous result by Gastpar et al. for the two-receiver BC.

This paper considers a random access system where each sender is in one of two possible states, active or not active, and the states are only known to the common receiver. Active senders encode data into independent information streams, a subset of which is decoded depending on the collective interference. An information-theoretic formulation of the problem is presented and the set of achievable rates is characterized with a guaranteed gap to optimality. Inner and outer bounds on the capacity region of a two-sender system are tight in the case of a binary-expansion deterministic channel and differ by less than one bit in the case of a Gaussian channel. In systems with an arbitrary number of senders, the symmetric scenario of equal access probabilities and received power constraints is studied and the system throughput, i.e., the maximum achievable expected sum rate, is characterized. It is shown that a simple coding scheme where active senders transmit a single message is optimum for a binary-expansion deterministic channel and achieves within one bit of the optimum in the case of a Gaussian channel. Finally, a comparison with the slotted ALOHA protocol is provided, showing that encoding rate adaptation at the transmitters achieves constant (rather than zero) throughput as the number of users tends to infinity.

A code for communication over the k-receiver additive white Gaussian noise broadcast channel with feedback is presented and analyzed using tools from the theory of linear quadratic Gaussian optimal control. It is shown that the performance of this code depends on the noise correlation at the receivers and it is related to the solution of a discrete algebraic Riccati equation. For the case of independent noises, the sum rate achieved by the proposed code, satisfying average power constraint P, is characterized as 1/2 log(1 + Pφ), where the coefficient φ ∈ [1, k] quantifies the power gain due to the presence of feedback. When specialized to the case of two receivers, this includes a previous result by Elia and strictly improves upon the code of Ozarow and Leung. When the noises are correlated, the pre-log of the sum-capacity of the broadcast channel with feedback can be strictly greater than one. It is established that for all noise covariance matrices of rank r the pre-log of the sum capacity is at most k - r + 1 and, conversely, there exists a noise covariance matrix of rank r for which the proposed code achieves this upper bound. This generalizes a previous result by Gastpar and Wigger for the two-receiver broadcast channel.

Motivated by the recently developed hybrid coding scheme for joint source-channel coding, this paper proposes a new coding scheme for noisy relay networks. The proposed coding scheme operates in a similar manner to the noisy network coding scheme, except that each relay node uses the hybrid coding interface to transmit a symbol-by-symbol function of the received sequence and its quantized version. This coding scheme unifies both amplify-forward and noisy network coding and can strictly outperform both. The potential of the hybrid coding interface for relaying is demonstrated through the diamond relay network and two-way relay channel examples.

A new analog-digital hybrid coding architecture for joint source-channel coding is proposed. The encoder generates a channel input by a symbol-by-symbol mapping of the observed (analog) source and its (digital) compression codeword, while the decoder reconstructs the source by a symbol-by-symbol mapping of the (analog) channel output and the decoded (digital) compression codeword from it. When applied to the problem of lossy communication of sources over the two-user discrete memoryless interference channel, this hybrid coding scheme achieves the best known performance and recovers as special cases several previous results on lossless and lossy communication over single hop networks.

The problem of determining the number of spatial degrees of freedom (d.o.f.) of the signals carrying information in a wireless network is reduced to the computation of the geometric variation of the environment with respect to the cut through which the information must flow. Physically, this has an appealing interpretation in terms of the diversity induced on the cut by the possible richness of the scattering environment. Mathematically, this variation is expressed as an integral along the cut, which we call cut-set integral, and whose scaling order is evaluated exactly in the case of planar networks embedded in arbitrary three-dimensional (3-D) environments. Presented results shed some new light on the problem of computing the capacity of wireless networks, showing a fundamental limitation imposed by the size of the cut through which the information must flow. In an attempt to remove what may appear as apparent inconsistencies with previous literature, we also discuss how our upper bounds relate to corresponding lower bounds obtained using the techniques of multihop, hierarchical cooperation, and interference alignment.

It is shown using first physical principles and without relying on stochastic fading channel models, that the number of spatial degrees of freedom available in planar wireless networks embedded in a three-dimensional propagation environment is limited by the spatial size of the cut that divides the environment into two parts. Specifically, in the case of propagation inside a cylinder of height h and base area n, containing n communicating source-destination node pairs, the number of available channels is at most proportional to h√n and hence, as the number of nodes increases, the per-user information capacity must follow an inverse square-root of n law.

This paper considers a slotted ALOHA random access system where users send packets to a common receiver with multipacket reception capability. A collection of m users access the shared medium independently of each other with probability p and, upon access, they choose an encoding rate. A collision occurs when the sum of the rates of all the users exceeds the capacity of the channel. We analytically characterize as a function of m and p the encoding rate which maximizes the expected global though put of the system. It is shown that for any value of p the throughput converges to one when m tends to infinity, hence there is no loss due to packet collisions. This is in striking contrast with the well known behavior of slotted ALOHA systems in which users cannot adjust the encoding rate. In that case the throughput decreases to zero as the number of users increases. Finally, assuming that users are selfish, we characterize the encoding rate which maximizes the expected individual throughput of each user, and show that the corresponding Nash equilibrium is not globally optimum.

An alternative characterization is given for the coding theorem by Han and Costa, which finds a set of admissible source pairs that can be transmitted reliably over the broadcast channel. The associated coding technique is conceptually simpler and the resulting admissible source region can be shown to include the Gray-Wyner distributed source coding region in a straightforward manner. Incidentally, this new characterization illustrates how the common part between the two random sources does not play any role in broadcasting correlated sources, unlike transmission of correlated sources over the multiple access channel.

It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order ofnusers wishing to establish pairwise independent communications at fixed wavelength inside a two-dimensional domain of size of the order ofn, there are an order ofncommunication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order ofradicn, so the per-user information capacity must follow an inverse square-root ofnlaw. This result shows that information-theoretic limits of wireless communication problems can be rigorously obtained without relying on stochastic fading channel models, but studying their physical geometric structure.

It is shown that the capacity scaling of three- dimensional wireless networks is subject to a degrees of freedom limitation which is due to the propagation laws of electromagnetic waves. By distributing uniformly an order of n users wishing to establish pairwise independent communications at fixed wavelength lambda inside a domain of (normalized) volume of the order of n, there are an order of n communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of n2/3, so the peruser information capacity must follow an inverse-cube root of n law.

"THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD" In this paper, we employ a broadcast transmission strategy for studying multiple access communication with no channel state information (CSI) at the transmitter. Users simultaneously encode their data into several streams that are then superimposed on top of each other. The receiver decodes a subset of the transmitted streams, dependent on the quality of the channel. We focus on two particular problems: first, we analyze communication over a Gaussian multiple access channel (MAC) with slow fading and no transmitter CSI. Users encode one stream per each fading state. We characterize the fundamental tradeoff between the achievable sum-rates in the various data streams. Next, we study transmission over a two- user synchronous Gaussian MAC in which users transmit in an uncoordinated and random manner. Each user superimposes two data streams, one high priority, ensuring part of the information is received reliably, and one high rate, opportunistically taking advantage of the channel when the other user is not transmitting. We study the performance limit for low and high SNR regimes.

We study the reliability of sequential codes in a two-state Markov fading AWGN channel under the assumption of noiseless feedback and an average power constraint. We present a capacity achieving scheme with a doubly exponential anytime reliability function with respect to delay for every bit. The scheme is represented by a hybrid control system at the encoder in which the discrete system dynamics evolves based only on the channel state information while the continuous part of the state at the encoder reflects the evolution of the message uncertainty at the decoder. Whereas the classical Schalkwijk-Kailath scheme achieves double exponential reliability by exploiting the average nature of the power constraint to combat atypicality of the AWGN noise, our scheme also uses it to combat atypical fading realizations