A.R. Calderbank

Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures

Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of layering as optimization decomposition, where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how layering as Optimization Decomposition provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures

Great expectations: the value of spatial diversity in wireless networks

The effect of spatial diversity on the throughput and reliability of wireless networks is examined. Spatial diversity is realized through multiple independently fading transmit/receive antenna paths in single-user communication and through independently fading links in multiuser communication. Adopting spatial diversity as a central theme, we start by studying its information-theoretic foundations, then we illustrate its benefits across the physical (signal transmission/coding and receiver signal processing) and networking (resource allocation, routing, and applications) layers. Throughout the paper, we discuss engineering intuition and tradeoffs, emphasizing the strong interactions between the various network functionalities.

Utility-optimal random-access control

This paper designs medium access control (MAC) protocols for wireless networks through the network utility maximization (NUM) framework. A network-wide utility maximization problem is formulated, using a collision/persistence-probabilistic model and aligning selfish utility with total social welfare. By adjusting the parameters in the utility objective functions of the NUM problem, we can also control the tradeoff between efficiency and fairness of radio resource allocation. We develop two distributed algorithms to solve the utility-optimal random-access control problem, which lead to random access protocols that have slightly more message passing overhead than the exponential-backoff protocols, but significant potential for efficiency and fairness improvement. We provide readily-verifiable sufficient conditions under which convergence of the proposed algorithms to a global optimality of network utility can be guaranteed, and numerical experiments that illustrate the value of the NUM approach to the complexity-performance tradeoff in MAC design.

Price-based distributed algorithms for rate-reliability tradeoff in network utility maximization

The current framework of network utility maximization for rate allocation and its price-based algorithms assumes that each link provides a fixed-size transmission pipe and each users utility is a function of transmission rate only. These assumptions break down in many practical systems, where, by adapting the physical layer channel coding or transmission diversity, different tradeoffs between rate and reliability can be achieved. In network utility maximization problems formulated in this paper, the utility for each user depends on both transmission rate and signal quality, with an intrinsic tradeoff between the two. Each link may also provide a higher (or lower) rate on the transmission pipes by allowing a higher (or lower) decoding error probability. Despite nonseparability and nonconvexity of these optimization problems, we propose new price-based distributed algorithms and prove their convergence to the globally optimal rate-reliability tradeoff under readily-verifiable sufficient conditions. We first consider networks in which the rate-reliability tradeoff is controlled by adapting channel code rates in each links physical-layer error correction codes, and propose two distributed algorithms based on pricing, which respectively implement the integrated and differentiated policies of dynamic rate-reliability adjustment. In contrast to the classical price-based rate control algorithms, in our algorithms, each user provides an offered price for its own reliability to the network, while the network provides congestion prices to users. The proposed algorithms converge to a tradeoff point between rate and reliability, which we prove to be a globally optimal one for channel codes with sufficiently large coding length and utilities whose curvatures are sufficiently negative. Under these conditions, the proposed algorithms can thus generate the Pareto optimal tradeoff curves between rate and reliability for all the users. In addition, the distributed algorithms and convergence proofs are extended for wireless multiple-inpit-multiple-output multihop networks, in which diversity and multiplexing gains of each link are controlled to achieve the optimal rate-reliability tradeoff. Numerical examples confirm that there can be significant enhancement of the network utility by distributively trading-off rate and reliability, even when only some of the links can implement dynamic reliability.

A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes

This paper proposes a deterministic compressed sensing matrix that comes by design with a very fast reconstruction algorithm, in the sense that its complexity depends only on the number of measurements n and not on the signal dimension N. The matrix construction is based on the second order Reed- Muller codes and associated functions. This matrix does not have RIP uniformly with respect to all k-sparse vectors, but it acts as a near isometry on k-sparse vectors with very high probability.

Content-Aware Distortion-Fair Video Streaming in Congested Networks

Internet is experiencing a substantial growth of video traffic. Given the limited network bandwidth resources, how to provide Internet users with good video playback quality-of-service (QoS) is a key problem. For video clips competing bandwidth, we propose an approach of Content-Aware distortion-Fair (CAF) video delivery scheme, which is aware of the characteristics of video frames and ensures max-min distortion-fair sharing among video flows. CAF leverages content-awareness to prioritize packet dropping during congestion. Different from bandwidth fair sharing, CAF targets end-to-end video playback quality fairness among users. The proposed CAF approach does not require rate-distortion modeling of the source, which is difficult to estimate. Instead, it exploits the temporal prediction structure of the video sequences along with a frame drop distortion metric to guide resource allocations and coordinations. Experimental results show that the proposed approach operates with limited overhead in computation and communication, and yields better QoS, especially when the network is congested.

Multiuser detection of alamouti signals

In a MIMO multiple-access channel where users employ Space-Time Block Codes (STBC), interference cancellation can be used to suppress co-channel interference and recover the desired signal of each user at the receiver. Leveraging the special properties of Alamouti matrices, we first show that spatial multiplexing of Alamouti signals retains the space-time diversity gain of Alamouti signaling using our proposed low-complexity Alamouti BLAST-MMSE (A-BLAST) Algorithm. Next, in contrast to traditional transmit diversity that focuses on STBC construction at the transmitter, this paper looks at transmit diversity from the perspective of the receiver. In other words, the receiver gets to choose the STBCiquests, which are favourable to the channel assuming a fixed BLAST receive algorithm. In a multiuserMAC setting, we first present a systematic methodology to exploit different decomposition structure in Alamouti matrices, each with different tradeoff between performance and decoding complexity using possibly different MIMO receive algorithms. We then demonstrate that the notion of angles (the inner product of two quaternionic vectors) between multiuser channels determines the performance of MIMO receive algorithms. As an application of the general theory, we transform the decoding problem for several types of Quasi-Orthogonal STBC (QOSTBC) into multiuser detection of virtual Alamouti users. Building upon our A-BLAST Algorithm, we propose new algorithms for decoding single-user and multiuser QOSTBC. In particular, we show that bit error probability is a function of the quaternionic angle between virtual users (for a single user) or multiple users. This angle varies with the type of QOSTBC and leads to a new form of adaptive modulation called code diversity, where feedback instructs the transmitter how to choose from a plurality of codes.

Utility-Optimal Medium Access Control: Reverse and Forward Engineering

This paper analyzes and designs medium access control (MAC) protocols for wireless ad-hoc networks through the network utility maximization (NUM) framework. We first reverse-engineer the current exponential backoff (EB) type of MAC protocols such as the BEB (binary exponential backoff) in the IEEE 802.11 standard through a non-cooperative game- theoretic model. This MAC protocol is shown to be implicitly maximizing, using a stochastic subgradient, a selfish local utility at each link in the form of expected net reward for successful transmission. While the existence of a Nash equilibrium can be established, neither convergence nor social welfare optimality is guaranteed due to the inadequate feedback mechanism in the EB protocol. This motivates the forward-engineering part of the paper, where a network-wide utility maximization problem is for- mulated, using a collision and persistence probability model and aligning selfish utility with total social welfare. By adjusting the parameters in the utility objective functions of the NUM problem, we can also control the tradeoff between efficiency and fairness of radio resource allocation through a rigorous and systematic design. We develop two distributed algorithms to solve the MAC design NUM problem, which lead to random access protocols that have slightly more message passing overhead than the current EB protocol, but significant potential for efficiency and fairness improvement. We provide readily-verifiable sufficient conditions under which convergence of the proposed algorithms to a global optimality of network utility can be guaranteed, and through numerical examples illustrate the value of the NUM approach to the complexity-performance tradeoff in MAC design.

Fast Optimal Decoding of Multiplexed Orthogonal Designs by Conditional Optimization

This paper focuses on conditional optimization as a decoding primitive for high rate space-time codes that are obtained by multiplexing in the spatial and code domains. The approach is a crystallization of the work of Hottinen which applies to space-time codes that are assisted by quasi-orthogonality. It is independent of implementation and is more general in that it can be applied to space-time codes such as the Golden Code and perfect space-time block codes, that are not assisted by quasi-orthogonality, to derive fast decoders with essentially maximum likelihood (ML) performance. The conditions under which conditional optimization leads to reduced complexity ML decoding are captured in terms of the induced channel at the receiver. These conditions are then translated back to the transmission domain leading to codes that are constructed by multiplexing orthogonal designs. The methods are applied to several block space-time codes obtained by multiplexing Alamouti blocks where it leads to ML decoding with complexity O(N 2) where N is the size of the underlying QAM signal constellation. A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML. The two design principles for perfect space-time codes are nonvanishing determinant of pairwise differences and cubic shaping, and it is cubic shaping that restricts the possible multiplexing structures. The new code shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity.

Diversity Embedded Space–Time Codes

Rate and diversity impose a fundamental tradeoff in wireless communication. High-rate space-time codes come at a cost of lower reliability (diversity), and high reliability (diversity) implies a lower rate. However, wireless networks need to support applications with very different quality-of-service (QoS) requirements, and it is natural to ask what characteristics should be built into the physical layer link in order to accommodate them. In this paper, we design high-rate space-time codes that have a high-diversity code embedded within them. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations while the embedded high-diversity code provides guarantees that at least part of the information is received reliably. We provide constructions of linear and nonlinear codes for a fixed transmit alphabet constraint. The nonlinear constructions are a natural generalization to wireless channels of multilevel codes developed for the additive white Gaussian noise (AWGN) channel that are matched to binary partitions of quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. The importance of set-partitioning to code design for the wireless channel is that it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain. We investigate the systems implications of embedded diversity codes by examining value to unequal error protection, rate opportunism, and packet delay optimization. These applications demonstrate that diversity-embedded codes have the potential to outperform traditional single-layer codes in moderate signal-to-noise (SNR) regimes.