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Bounds on diversity for coded systems on non-ergodic channels
On a single-antenna ergodic fading channel, a frame sees different channel realizations at each time epoch. This gives a Nakagami distribution of high order (represented by the sum of the khjk2) at the output of the detector and thus gives a high order of diversity. The diversity order that can be achieved by a ST-BICM on such channels is thus mainly limited by the minimum Hamming distance dmin of the channel code. Over block-fading channels with a limited number of states, the situation is different. In the sequel, we will call BO-channel the binary-oriented channel with input ci and output (ci) as observed by the channel encoder and the channel decoder.
Cooperative communications protocols
After the authors in [66, 67] introduced the concept of cooperative diversity, many papers proposed cooperation protocols that define the way the cooperation between users is performed. These protocols can be classified into two major categories, that are amplify-andforward (AF) and decode-and-forward (DF). Note that the large majority of the existing designs we will recall in the sequel are based on the so-called “Diversity-Multiplexing Tradeoff” (DMT) of the channel [68]. The DMT is a piece-wise linear function that represents, at very high signal-to-noise ratios, the tradeoff between the maximum achievable rate (as a function of the signal-to-noise ratio) and the maximal achievable diversity order over the wireless channel. Although the DMT bound gives an insight on the superiority of a given protocol (or a given antenna configuration for MIMO systems) and allows for the design of optimal space-time precoders for uncoded systems, its relevance as a design tool for coded modulations with iterative decoding is arguable.
Amplify-and-forward protocols
In these protocols, the relays scale the signals received from the source (or by other relays) and forward them to the destination (or to other relays) without other treatment. These protocols are easy to implement in practical communication systems, as the computational complexity they introduce at the relay is limited to the scaling operation. The orthogonal amplify-and-forward (OAF) protocol was first introduced in [69] for the single-relay case. By orthogonal we mean that the source and the relay do not send data simultaneously. The second major work concerning this family of protocols is the framework established in [70] for the single-relay case. The authors proposed three amplify-and-forward protocols that are:
Protocol I: the source broadcasts a signal to both the relay and the destination in the first phase. In the second phase, the relay scales the signal and forwards it to the destination, while the source transmits another message to the destination. This protocol is also known as the non-orthogonal amplify-and-forward (NAF) protocol [71].
Protocol II: the source broadcasts a signal to both the relay and the destination in the first phase like in Protocol I. In the second phase, only the relay scales the signal it received in the previous phase and forwards it to the destination. This protocol is the OAF protocol introduced in [69].
Protocol III: the source sends a signal only to the relay in the first phase. The second phase is similar to the second phase in Protocol I. In addition to introducing these protocols, the authors discussed and analyzed some information theoretical aspects of cooperative protocols that brought insight to the behavior of such systems. From these three protocol, Protocol I caught the attention of the researchers in the community as it allows for high data rates (the source always transmits). Indeed, in [71], it is shown that the NAF protocol outperforms the AF protocol for high data rates. However, for the case of more than one relay, the NAF protocol suffers from a limitation , as half of the symbols in the cooperation frame are protected. For this reason, the authors in [72] proposed the slotted amplify-and-forward (SAF) scheme; by allowing inter-relay communication (see Fig. 3.1), on can protect out of + 1 symbols. For this reason, the SAF scheme largely outperforms the -relay NAF scheme for high data rates. Many space-time code design for uncoded fading channels for the AF protocolswere proposed, among them [73] [74] [75, 76], but optimal space-time codes for uncoded systems can be found in [72] [77].
Table of contents :
List of Figures
List of Tables
Résumé de la thèse en Français
Introduction
Chapitre 1: Notions de théorie de l’information
Chapitre 2: Modulations codées pour les systèmes à antennes multiples
Chapitre 3: Modulations codées pour les systèmes coopératifs
Chapitre 4: Conception de turbo codes irréguliers pour les canaux à évanouissements par blocs
Introduction
1 Generalities
1.1 Introduction
1.2 Information theory of fading channels
1.3 Bit-interleaved coded modulation (BICM) with iterative decoding
1.3.1 Structure of the BICM transmitter
1.3.2 The BICM iterative receiver
1.4 Bounds on diversity for coded systems on non-ergodic channels
1.5 Conclusions
2 Coded modulations for the multipleantenna channel
2.1 Introduction
2.2 A brief historical note
2.3 Upper bound on the frame error rate for uncoded space-time signaling
2.4 System model and notations
2.5 Diversity bounds for coded multiple-antenna systems
2.6 Space-time precoders based on information outage minimization
2.6.1 Introduction
2.6.2 Linear precoding designs
2.6.3 Simulation results
2.7 Space-time precoders based on the Alamouti scheme
2.7.1 Introduction
2.7.2 Matrix-Alamouti scheme
2.7.3 Iterative joint detection and decoding
2.7.4 Simulation results
2.8 Outage-approaching turbo codes for the multiple-antenna channels
2.8.1 Introduction
2.8.2 Code multiplexing over channel states
2.8.3 Word error rate performance with nt = 2
2.8.4 Linear precoding via DNA rotations with nt = 4
2.9 Conclusions
3 Coded modulations for the amplifyand- forward cooperative channel
3.1 Introduction
3.2 Cooperative communications protocols
3.2.1 Amplify-and-forward protocols
3.2.2 Decode-and-forward protocols
3.3 Space-time bit-interleaved coded modulations for the amplify-and-forward cooperative channel
3.4 System model and parameters
3.5 The diversity of coded modulations over precoded SAF channels
3.5.1 Matryoshka block-fading channels
3.5.2 Precoded SAF channel models and associated bounds
3.6 Coding strategies
3.6.1 Simulation results
3.7 Code multiplexing over channel states for the half-duplex NAF cooperative channel
3.7.1 Simulation results
3.8 Conclusions
4 Design of irregular turbo codes for block-fading channels
4.1 Introduction
4.2 Basics on Irregular Turbo Codes
4.2.1 Density Evolution in AWGN
4.2.2 Numerical results for AWGN
4.3 Irregular Turbo Codes over Block-Fading Channels
4.3.1 Density evolution on BF channel
4.3.2 Numerical results on BF channel
4.4 Conclusions
Conclusions
