We develop and analyze low-complexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals' relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplify-and-forward and decode-and-forward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signal-to-noise ratio (SNR) regime. Except for fixed decode-and-forward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., second-order diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to half-duplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks-wherever space constraints preclude the use of physical arrays-the performance characterizations reveal that large power or energy savings result from the use of these protocols.

Cooperative diversity in wireless networks: Efficient protocols and outage behavior

Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination's channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static 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 and multidestination networks such as multiaccess and broadcast relay channels.

Cooperative strategies and capacity theorems for relay networks

We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

Capacity Limits of Optical Fiber Networks

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

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Multi-Cell MIMO Cooperative Networks: A New Look at Interference

Differential-phase-shift keying (DPSK) has recently been used to reach record distances in long-haul lightwave communication systems. This paper will review theoretical, as well as implementation, aspects of DPSK, and discuss experimental results.

Optical phase-shift-keyed transmission

The spectral efficiency of mobile radio networks can be improved by allowing each mobile station to act as a relay for one other mobile station. One can expect further performance improvement if each relay aids not just a single mobile station, but many simultaneously. We attempt to quantify this improvement by introducing the multiple-access relay channel (MARC) and deriving capacity results for it. Capacity outer and inner bounds for it are derived.

On the white Gaussian multiple-access relay channel

New methods are presented to protect maximum runlength-limited sequences against random and burst errors and to avoid error propagation. The methods employ parallel conversion techniques and enumerative coding algorithms that transform binary user information into constrained codewords. The new schemes have a low complexity and are very efficient. The approach can be used for modulation coding in recording systems and for synchronization and line coding in communication systems. The schemes enable the usage of high-rate constrained codes, as error control can be provided with similar capabilities as for unconstrained sequences.

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Maximum runlength-limited codes with error control capabilities

Several optical modulation and detection schemes are compared by computing their spectral efficiencies over additive white Gaussian noise channels. The bandwidth savings of differential quadrature phase-shift keying (D-QPSK) over both direct-detection on-off keying and differential binary phase-shift keying suggest that D-QPSK can improve the reach and efficiency of wavelength-division multiplexing systems. To test the theory, Reed-Solomon and low-density parity-check forward error correction codes are designed and evaluated. The codes generally behave as expected, except that for D-QPSK the gains are hampered by the differential detector. It is further shown that neither multiple-symbol differential detection nor decision-feedback detection is attractive when using strong codes.

Spectral efficiency of coded phase-shift keying for fiber-optic communication

We present a systematic procedure for mapping data sequences into codewords of a prefix-synchronized code (PS-code), as well as for performing the inverse mapping. A PS-code, proposed by Gilbert (1960), belongs to a subclass of comma-free codes and is useful to recover word synchronization when errors have occurred in the stream of codewords. A PS-code is defined as a set of codewords with the property that each codeword has a known sequence as a prefix, followed by a coded data sequence in which this prefix is not allowed to occur. The largest PS-code among all PS-codes of the same code length is called a maximal prefix-synchronized code (MPS-code). We develop an encoding and decoding algorithm for Gilbert's MPS-code with a prefix of the form 11...10 and extend the algorithm to the class PS-codes of which the prefix is self-uncorrelated. The computational complexity of the entire mapping process is proportional to the length of the codewords.

On the construction of maximal prefix-synchronized codes

The sequence replacement technique converts an input sequence into a constrained sequence in which a prescribed subsequence is forbidden to occur. Several coding algorithms are presented that use this technique for the construction of maximum run-length limited sequences. The proposed algorithms show how all forbidden subsequences can be successively or iteratively removed to obtain a constrained sequence and how special subsequences can be inserted at predefined positions in the constrained sequence to represent the indices of the positions where the forbidden subsequences were removed. Several modifications are presented to reduce the impact of transmission errors on the decoding operation, and schemes to provide error control are discussed as well. The proposed algorithms can be implemented efficiently, and the rates of the constructed codes are close to their theoretical maximum. As such, the proposed algorithms are of interest for storage systems and data networks.

A.J. van Wijngaarden

Papers

On the white Gaussian multiple-access relay channel

Maximum runlength-limited codes with error control capabilities

Spectral efficiency of coded phase-shift keying for fiber-optic communication

On the construction of maximal prefix-synchronized codes

Construction of Maximum Run-Length Limited Codes Using Sequence Replacement Techniques