Channel Capacity

A low-density parity-check code is a code specified by a parity-check matrix with the following properties : each column contains a small fixed numberj > 3 of I's and each row contains a small fixed number k > j of 1's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j. When used with maximum likelihood decoding on a snfhciently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixedj.

Coding strategies that exploit terminal cooperation are developed for relay networks. Two basic schemes are studied: the relays multi-hop the source message to the destination, or they transmit compressed channel outputs to the destination. Strategies that mix these schemes are also considered. The multihopping is done in a sophisticated way: the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For compression, the relays take advantage of the statistical dependence between their channel outputs and the destination's channel output. The strategies are applied to several wireless channels, and it is shown that one can approach capacity if the terminals form two closely spaced clusters. One can further achieve the ergodic capacity with phase fading if the relays are in a region near the source terminal, and if phase information is available only locally. The ergodic capacity results generalize to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasistatic fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource networks such as multi-access and broadcast relay channels.

We investigate the effects of fading correlations in multielement antenna (MEA) communication systems. Pioneering studies showed that if the fades connecting pairs of transmit and receive antenna elements are independently, identically distributed, MEA's offer a large increase in capacity compared to single-antenna systems. An MEA system can be described in terms of spatial eigenmodes, which are single-input single-output subchannels. The channel capacity of an MEA is the sum of capacities of these subchannels. We will show that the fading correlation affects the MEA capacity by modifying the distributions of the gains of these subchannels. The fading correlation depends on the physical parameters of MEA and the scatterer characteristics. In this paper, to characterize the fading correlation, we employ an abstract model, which is appropriate for modeling narrow-band Rayleigh fading in fixed wireless systems.

Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We use an information-theoretic approach to compute the optimal amount of training as a function of the received signal-to-noise ratio, fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. As side results, we obtain the worst-case power-constrained additive noise in a matrix-valued additive noise channel, and show that training-based schemes are highly suboptimal at low SNR.

Although the capacity of multiple-input/multipleoutput (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in round-robin ZFBF and proportional-fair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.

We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li et al., who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary networks and robust networking. For networks which are restricted to using linear network codes, we find necessary and sufficient conditions for the feasibility of any given set of connections over a given network. We also consider the problem of network recovery for nonergodic link failures. For the multicast setup we prove that there exist coding strategies that provide maximally robust networks and that do not require adaptation of the network interior to the failure pattern in question. The results are derived for both delay-free networks and networks with delays.

We analyze a mobile wireless link comprising M transmitter and N receiver antennas operating in a Rayleigh flatfading environment. The propagation coefficients between pairs of transmitter and receiver antennas are statistically independent and unknown; they remain constant for a coherence interval of T symbol periods, after which they change to new independent values which they maintain for another T symbol periods, and so on. Computing the link capacity, associated with channel coding over multiple fading intervals, requires an optimization over the joint density of T 1 M complex transmitted signals. We prove that there is no point in making the number of transmitter antennas greater than the length of the coherence interval: the capacity for M > T is equal to the capacity for M = T. Capacity is achieved when the T 2 M transmitted signal matrix is equal to the product of two statistically independent matrices: a T 2 T isotropically distributed unitary matrix times a certain T 2 M random matrix that is diagonal, real, and nonnegative. This result enables us to determine capacity for many interesting cases. We conclude that, for a fixed number of antennas, as the length of the coherence interval increases, the capacity approaches the capacity obtained as if the receiver knew the propagation coefficients.

The present review focuses on the utility of the amplitude of P3 of as a measure of processing capacity and mental workload. The paper starts with a brief outline of the conceptual framework underlying the relationship between P3 amplitude and task demands, and the cognitive task manipulations that determine demands on capacity. P3 amplitude results are then discussed on the basis of an extensive review of the relevant literature. It is concluded that although it has often been assumed that P3 amplitude depends on the capacity for processing task relevant stimuli, the utility of P3 amplitude as a sensitive and diagnostic measure of processing capacity remains limited. The major factor that prompts this conclusion is that the two principal task variables that have been used to manipulate capacity allocation, namely task difficulty and task emphasis, have opposite effects on the amplitude of P3. I suggest that this is because, in many tasks, an increase in difficulty transforms the structure or actual content of the flow of information in the processing systems, thereby interfering with the very processes that underlie P3 generation. Finally, in an attempt to theoretically integrate the results of the reviewed studies, it is proposed that P3 amplitude reflects activation of elements in a eventcategorization network that is controlled by the joint operation of attention and working memory.

We investigate robust wireless communication in high-scattering propagation environments using multi-element antenna arrays (MEA's) at both transmit and receive sites. A simplified, but highly spectrally efficient space-time communication processing method is presented. The user's bit stream is mapped to a vector of independently modulated equal bit-rate signal components that are simultaneously transmitted in the same band. A detection algorithm similar to multiuser detection is employed to detect the signal components in white Gaussian noise (WGN). For a large number of antennas, a more efficient architecture can offer no more than about 40% more capacity than the simple architecture presented. A testbed that is now being completed operates at 1.9 GHz with up to 16 quadrature amplitude modulation (QAM) transmitters and 16 receive antennas. Under ideal operation at 18 dB signal-to-noise ratio (SNR), using 12 transmit antennas and 16 receive antennas (even with uncoded communication), the theoretical spectral efficiency is 36 bit/s/Hz, whereas the Shannon capacity is 71.1 bit/s/Hz. The 36 bits per vector symbol, which corresponds to over 200 billion constellation points, assumes a 5% block error rate (BLER) for 100 vector symbol bursts. He has been involved with data communications research on many kinds of systems including wireless communications and optical communications systems. He has done extensive research on pointto-point systems as well as on networks. He is currently with Lucent Technologies, Bell Labs Innovations. He is temporarily on leave from wireless communication research to work in the area of optical communication theory, where he is concentrating on analyzing both polarization mode dispersion and fiber nonlinearities. He has taught at

In this report we use a previously developed nonlinear dynamic model of TCP to analyze and design Active Queue Management (AQM) Control Systems using RED. First, we linearize the interconnection of TCP and a bottlenecked queue and discuss its feedback properties in terms of network parameters such as link capacity, load and round-trip time. Using this model, we next design an AQM control system using the random early detection (RED) scheme by relating its free parameters such as the low-pass filter break point and loss probability profile to the network parameters. We present guidelines for designing linearly stable systems subject to network parameters like propogation delay and load level. Robustness to variations in system loads is a prime objective. We present ns simulations to support our analysis.

Wideband analog signals push contemporary analog-to-digital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the bandlimit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its bandlimit in Hz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W Hz. In contrast with Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system's performance that supports the empirical observations.

Classically, sending more than one bit of information requires manipulation of more than one two-state particle. We demonstrate experimentally that one can transmit one of three messages, i.e., 1 "trit" ഠ 1.58 bit, by manipulating only one of two entangled particles. The increased channel capacity is proven by transmitting ASCII characters in five trits instead of the usual 8 bits. [S0031-9007(96)00478-4]

We investigate the performance and design of free-space optical (FSO) communication links over slow fading channels from an information theory perspective. A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence and pointing errors is derived. Unlike earlier work, our model considers the effect of beam width, detector size, and jitter variance explicitly. Expressions for the outage probability are derived for a variety of atmospheric conditions. For given weather and misalignment conditions, the beam width is optimized to maximize the channel capacity subject to outage. Large gains in achievable rate are realized versus using a nominal beam width. In light fog, by optimizing the beam width, the achievable rate is increased by 80% over the nominal beam width at an outage probability of 10 −5 . Well-known error control codes are then applied to the channel and shown to realize much of the achievable gains.

Fair scheduling of delay and rate-sensitive packet flows over a wireless channel is not addressed effectively by most contemporary wireline fair-scheduling algorithms because of two unique characteristics of wireless media: 1) bursty channel errors and 2) location-dependent channel capacity and errors. Besides, in packet cellular networks, the base station typically performs the task of packet scheduling for both downlink and uplink flows in a cell; however, a base station has only a limited knowledge of the arrival processes of uplink flows. In this paper, we propose a new model for wireless fair scheduling based on an adaptation of fluid fair queueing (FFQ) to handle location-dependent error bursts. We describe an ideal wireless fair-scheduling algorithm which provides a packetized implementation of the fluid mode, while assuming full knowledge of the current channel conditions. For this algorithm, we derive the worst-case throughput and delay bounds. Finally, we describe a practical wireless scheduling algorithm which approximates the ideal algorithm. Through simulations, we show that the algorithm achieves the desirable properties identified in the wireless FFQ model.

The "covariance" of complex random variables and processes, when defined consistently with the corresponding notion for real random variables, is shown to be detc!rmioed by the usual (complex) covariance together with a quantity called the pseudo-covariance. A characterization of uncorrelatedness and wide-sense stationarity in terms of covariance and pseudocovariance is given. Complex random variables and processes with a vanishing pseudo-covariaqce are called proper. It is shown that properness is preserved under affine transformations and that the complex-multivariate Gaussian density assumes a natural form only for proper random variables. The maximumsotropy theorem is generalized to the complex-multivariate case. The differential entropy of a complex random vector with a tixed correlation matrix is shown to be maximum, if and only if the random vector is proper, Gaussian and zero-mean. The notion of chulur si'utio-is introduced. For the class of proper complex random processes, a discrete Fourier transform correspondence is derived dating circular stationarity in the time domain to uncomlatedness in the fmquency domain. As an application of the theory, the capacity of a discrete-time channel with complex inputs, proper complex additive white Gaussian noise, and a finite complex unit-sample response is determined. This derivation is considerably simpler than an earlier derivation for the red discrete-time Gaussian channel with intersymbol interference, whose capacity is obtained as a by-product of the results for the complex channel.

As the cellular and PCS world collides with Wireless LANs and Internet-based packet data, new networking approaches will support the integration of voice and data on the composite infrastructure of cellular base stations and Ethernet-based wireless access points. This paper highlights some of the past accomplishments and promising research avenues for an important topic in the creation of future wireless networks. In this paper, we address the issue of cross-layer networking, where the physical and MAC layer knowledge of the wireless medium is shared with higher layers, in order to provide efficient methods of allocating network resources and applications over the Internet. In essence, future networks will need to provide "impedance matching" of the instantaneous radio channel conditions and capacity needs with the traffic and congestion conditions found over the packet-based world of the Internet. Further, such matching will need to be coordinated with a wide range of particular applications and user expectations, making the topic of cross-layer networking an increasingly important one for the evolving wireless build-out.

We consider dynamic routing and power allocation for a wireless network with time-varying channels. The network consists of power constrained nodes that transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be transmitted through the network to their destinations. We establish the capacity region of all rate matrices (λij) that the system can stably support-where λij represents the rate of traffic originating at node i and destined for node j. A joint routing and power allocation policy is developed that stabilizes the system and provides bounded average delay guarantees whenever the input rates are within this capacity region. Such performance holds for general arrival and channel state processes, even if these processes are unknown to the network controller. We then apply this control algorithm to an ad hoc wireless network, where channel variations are due to user mobility. Centralized and decentralized implementations are compared, and the stability region of the decentralized algorithm is shown to contain that of the mobile relay strategy developed by Grossglauser and Tse (2002).

In a packet network, the terms bandwidth and throughput often characterize the amount of data that the network can transfer per unit of time. Bandwidth estimation is of interest to users wishing to optimize end-to-end transport performance, overlay network routing, and peer-to-peer file distribution. Techniques for accurate bandwidth estimation are also important for traffic engineering and capacity planning support. Existing bandwidth estimation tools measure one or more of three related metrics: capacity, available bandwidth, and bulk transfer capacity. Currently available bandwidth estimation tools employ a variety of strategies to measure these metrics. In this survey we review the recent bandwidth estimation literature focusing on underlying techniques and methodologies as well as open source bandwidth measurement tools.

Integrated cellular and ad hoc relaying systems (iCAR) is a new wireless system architecture based on the integration of cellular and modern ad hoc relaying technologies. It addresses the congestion problem due to unbalanced traffic in a cellular system and provides interoperability for heterogeneous networks. The iCAR system can efficiently balance traffic loads between cells by using ad hoc relaying stations (ARS) to relay traffic from one cell to another dynamically. This not only increases the system's capacity cost effectively, but also reduces transmission power for mobile hosts and extends system coverage. In this paper, we compare the performance of the iCAR system with conventional cellular systems in terms of the call blocking/dropping probability, throughput, and signaling overhead via analysis and simulation. Our results show that with a limited number of ARSs and some increase in the signaling overhead (as well as hardware complexity), the call blocking/dropping probability in a congested cell and the overall system can be reduced.

Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory.

This correspondence presents two variable-rate encoding algorithms that achieve capacity for the ( ) constraint when = 2 +1, or when +1 is not prime. The first algorithm, symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran et al. In addition to achieving capacity for ( 2 +1) constraints, it comes close to capacity in other cases. The second algorithm is based on interleaving and is a generalized version of the bit stuffing algorithm introduced by Bender and Wolf. This method uses fewer than biased bit streams to achieve capacity for ( ) constraints with + 1 not prime. In particular, the encoder for ( + 2 1) constraints 2 requires only biased bit streams.

Multiple-input multiple output (MIMO) communication architecture has recently emerged as a new paradigm for wireless communications in rich multipath environment, which has spectral efficiencies far beyond those offered by conventional techniques. Channel capacity of the MIMO architecture in independent Rayleigh channels scales linearly as the number of antennas. However, the correlation of a real-world wireless channel may result in a substantial degradation of the MIMO architecture performance. In this letter, we investigate the MIMO channel capacity in correlated channels using the exponential correlation matrix model. We prove that, for this model, increase in correlation is equivalent to decrease in signal-to-noise ratio (SNR). For example, = 0 7 is the same as 3-dB decrease in SNR.

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0 5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.

Path loss of an underwater acoustic communication channel depends not only on the transmission distance, but also on the signal frequency. As a result, the useful bandwidth depends on the transmission distance, a feature that distinguishes an underwater acoustic system from a terrestrial radio one. This fact influences the design of an acoustic network: a greater information throughput is available if messages are relayed over multiple short hops instead of being transmitted directly over one long hop. We asses the bandwidth dependency on the distance using an analytical method that takes into account physical models of acoustic propagation loss and ambient noise. A simple, single-path time-invariant model is considered as a first step. To assess the fundamental bandwidth limitation, we take an information-theoretic approach and define the bandwidth corresponding to optimal signal energy allocation -one that maximizes the channel capacity subject to the constraint that the transmission power is finite. Numerical evaluation quantifies the bandwidth and the channel capacity, as well as the transmission power needed to achieve a pre-specified SNR threshold, as functions of distance. These results lead to closed-form approximations, which may become useful tools in the design and analysis of acoustic networks.

• communication network with nodes connected by wireless links • multiple flows, from source to destination nodes • total traffic on each link limited by link capacity • link capacity is function of communication resource variables such as power, bandwidth, which are limited goal: find optimal operation of network, i.e., do simultaneous routing and resource allocation (SRRA) IPAM Workshop, 4/18/02 1 IPAM Workshop, 4/18/02

We present a theory, based on statistical mechanics, to evaluate analytically the performance of uncoded, fully synchronous, randomly spread code-division multiple-access (CDMA) multiuser detectors with additive white Gaussian noise (AWGN) channel, under perfect power control, and in the large-system limit. Application of the replica method, a tool developed in the literature of statistical mechanics, allows us to derive analytical expressions for the bit-error rate, as well as the multiuser efficiency, of the individually optimum (IO) and jointly optimum (JO) multiuser detectors over the whole range of noise levels. The information-theoretic capacity of randomly spread CDMA channel and the performance of decorrelating and linear minimum mean-square error (MMSE) detectors are also derived in the same replica formulation, thereby demonstrating validity of the statistical-mechanical approach.

The IEEE 802.11 MAC protocol provides shared access to a wireless channel. This paper uses an analytic model to study the channel capacity -i.e., maximum throughput -when using the basic access (two-way handshaking) method in this protocol. It provides closed-form approximations for the probability of collision p, the maximum throughput S and the limit on the number of stations in a wireless cell.

Dense coding is arguably the protocol that launched the field of quantum communication [1]. Today, however, more than a decade after its initial experimental realization [2], the channel capacity remains fundamentally limited as conceived for photons using linear elements. Bob can only send to Alice three of four potential messages due to the impossibility of performing the deterministic discrimination of all four Bell states with linear optics [3, 4], reducing the attainable channel capacity from 2 to log 2 3 ≈ 1.585 bits. However, entanglement in an extra degree of freedom enables the complete and deterministic discrimination of all Bell states [5-7]. Using pairs of photons simultaneously entangled in spin and orbital angular momentum [8, 9], we demonstrate the quantum advantage of the ancillary entanglement. In particular, we describe a dense-coding experiment with the largest reported channel capacity and, to our knowledge, the first to break the conventional linear-optics threshold. Our encoding is suited for quantum communication without alignment [10] and satellite communication.

The information rate of finite-state source/channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence, followed by a forward sum-product recursion on the joint source/channel trellis. This method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite-state approximations. Further upper and lower bounds can be computed by reduced-state methods.

We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers while ensuring mutual information-theoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to both channel models. The difference is in the input distributions over which the expression is optimized. The inner bound rate regions are achieved by random binning techniques. For the broadcast channel, a double-binning coding scheme allows for both joint encoding and preserving of confidentiality. Furthermore, we show that, for a special case of the interference channel, referred to as the switch channel, derived bounds meet. Finally, we describe several transmission schemes for Gaussian interference channels and derive their achievable rate regions while ensuring mutual information-theoretic secrecy. An encoding scheme in which transmitters dedicate some of their power to create artificial noise is proposed and shown to outperform both time-sharing and simple multiplexed transmission of the confidential messages.

In this correspondence, we consider the problem of maximizing sum rate of a multiple-antenna Gaussian broadcast channel (BC). It was recently found that dirty-paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e., the optimal transmit covariance structure) given the channel conditions and power constraint must be found. However, obtaining the optimal transmission policy when employing dirty-paper coding is a computationally complex nonconvex problem. We use duality to transform this problem into a well-structured convex multiple-access channel (MAC) problem. We exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the MAC, which can easily be mapped to the optimal BC policies.

We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an information-theoretic constructive scheme for obtaining an achievable rate region in such networks. Many well-known capacity-defining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reverselydegraded relay channels, the Gaussian multiple-access channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities.

Anastomosing rivers constitute an important category of multi-channel rivers on alluvial plains. Most often they seem to Ž. form under relatively low-energetic conditions near a local base level. It appears to be impossible to define anastomosing rivers unambiguously on the basis of channel planform only. Therefore, the following definition, which couples floodplain geomorphology and channel pattern, is proposed in this paper: an anastomosing riÕer is composed of two or more interconnected channels that enclose floodbasins. This definition explicitly excludes the phenomenon of channel splitting by convex-up bar-like forms that characterize braided channels. In present definitions of anastomosing rivers, lateral stability of channels is commonly coupled with their multi-channel character. Here, it is suggested that these two properties be uncoupled. At the scale of channel belts, the terms 'straight', 'meandering' and 'braided' apply, whereas at a larger scale, a river can be called anastomosing if it meets the definition given above. This means that, straight, meandering and braided channels may all be part of an anastomosing river system. Straight channels are defined by a sinuosity index; i.e., the ratio of the distance along the channel and the distance along the channel-belt axis is less than 1.3. They are the type of channel that most commonly occurs in combination with anastomosis. The occurrence of straight channels is favoured by low stream power, basically a product of discharge and gradient, and erosion-resistant banks. Anastomosing rivers are usually formed by avulsions, i.e., flow diversions that cause the formation of new channels on Ž. the floodplain. As a product of avulsion, anastomosing rivers essentially form in two ways: 1 by formation of bypasses, Ž. while bypassed older channel-belt segments remain active for some period; and 2 by splitting of the diverted avulsive flow, leading to contemporaneous scour of multiple channels on the floodplain. Both genetic types of anastomosis may coexist in one river system, but whereas the first may be a long-lived floodplain-wide phenomenon, the latter only represents a stage in the avulsion process on a restricted part of the floodplain. Long-lived anastomosis is caused by frequent avulsions andror slow abandonment of old channels. Avulsions are primarily driven by aggradation of the channel belt andror loss of channel capacity by in-channel deposition. Both processes are favoured by a low floodplain gradient. Also of influence are a number of avulsion triggers such as extreme floods, log and ice jams, and in-channel aeolian dunes. Although some of these triggers are associated with a specific climate, the occurrence of anastomosis is not. A rapid rise of base level is conductive to anastomosis, but is not a necessary condition.