Information Theory and Reliable Communication

Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

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Bit-Interleaved Coded Modulation

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.

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Wireless Information-Theoretic Security

Optical wireless communication (OWC) refers to transmission in unguided propagation media through the use of optical carriers, i.e., visible, infrared (IR), and ultraviolet (UV) bands. In this survey, we focus on outdoor terrestrial OWC links which operate in near IR band. These are widely referred to as free space optical (FSO) communication in the literature. FSO systems are used for high rate communication between two fixed points over distances up to several kilometers. In comparison to radio-frequency (RF) counterparts, FSO links have a very high optical bandwidth available, allowing much higher data rates. They are appealing for a wide range of applications such as metropolitan area network (MAN) extension, local area network (LAN)-to-LAN connectivity, fiber back-up, backhaul for wireless cellular networks, disaster recovery, high definition TV and medical image/video transmission, wireless video surveillance/monitoring, and quantum key distribution among others. Despite the major advantages of FSO technology and variety of its application areas, its widespread use has been hampered by its rather disappointing link reliability particularly in long ranges due to atmospheric turbulence-induced fading and sensitivity to weather conditions. In the last five years or so, there has been a surge of interest in FSO research to address these major technical challenges. Several innovative physical layer concepts, originally introduced in the context of RF systems, such as multiple-input multiple-output communication, cooperative diversity, and adaptive transmission have been recently explored for the design of next generation FSO systems. In this paper, we present an up-to-date survey on FSO communication systems. The first part describes FSO channel models and transmitter/receiver structures. In the second part, we provide details on information theoretical limits of FSO channels and algorithmic-level system design research activities to approach these limits. Specific topics include advances in modulation, channel coding, spatial/cooperative diversity techniques, adaptive transmission, and hybrid RF/FSO systems.

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Survey on Free Space Optical Communication: A Communication Theory Perspective

Sphere Packings, Lattices and Groups

This paper deals with 2/sup l/-ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a large space of rate combinations such that MLC and full maximum-likelihood decoding (MLD) can approach capacity. It is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and, therefore, require the huge complexity of MLD. The capacity rule, the balanced distances rules, and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design. Simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies. Moreover, topics relevant in practical applications such as signal set labeling, dimensionality of the constituent constellation, and hard-decision decoding are emphasized. Bit interleaved coded modulation, proposed by Caire et al. (see ibid., vol.44, p.927-46, 1998), is reviewed in the context of MLC. Finally, the combination of signal shaping and coding is discussed. Significant shaping gains are achievable in practice only if these design rules are taken into account.

/pdf/multilevel-codes-theoretical-concepts-and-practical-design-5ec1khobkg.pdf

Multilevel codes: theoretical concepts and practical design rules

The recently proposed Turbo codes are applied to bandwidth efficient modulation schemes via multilevel coding. For this purpose, Turbo codes are extended for a wide range of fine tunable rates by puncturing. A straightforward derivation of iterative Turbo decoding and the concept of extrinsic information is presented. New design rules for multilevel codes with arbitrary component codes and codeword lengths are derived from information theory. Simulation results show that application of Turbo codes to properly designed multilevel coding schemes leads to digital transmission schemes with high power and bandwidth efficiency.

Power and bandwidth efficient digital communication using turbo codes in multilevel codes

Important issues for coded modulation in practice are derived from information theoretic parameters. Optimality of multilevel coding as well as various rules to assign rates to the individual component codes are discussed. Moreover, suitable dimensionality of the signal constellation used for coding is considered. All phenomena predicted from information theory are confirmed by simulation results. Finally, optimum combination of coding and signal shaping is derived. Noticeable shaping gains are only achievable if presented rules are taken into account.

http://ieeexplore.ieee.org/iel3/4477/12707/00586754.pdf

Multilevel coding: aspects from information theory

Während der ersten 25 Jahre nach der Begründung der Informationstheorie durch C.E. Shannon vor jetzt genau 50 Jahren konzentrierte sich die Entwicklung der Kanalcodierung nahezu ausschlieÿlich auf die binäre digitale Übertragung, also z.B. binäre Amplituden bzw. Phasenmodulation (BPSK), quaternäre Phasenmodulation mit unabhängiger binärer Übertragung in beiden Quadraturkomponenten (QPSK mit Gray Zuordnung bzw. 4 QAM). Man stellte jedoch bald fest, daÿ eine direkte Anwendung von binären Codes zur Vorwärtsfehlerkorrektur (Forward Error Correction: FEC) gemäÿ Bild 1 auf höherstu ge Übertragungsverfahren, die eine höhere Bandbreitene zienz (Informations uÿ bit s je Hz Signalbandbreite) bieten, wenig e zient ist. Dieser E ekt wird anhand eines Vergleichs von Übertragungsverfahren im Leistungs Bandbreiten Diagramm (LBD) für den Kanal mit Störung durch weiÿes Gauÿ'sches Rauschen (AWGN Kanalmodell) deutlich, das in Bild 2 dargestellt ist. Hierbei wird die Leistungse zienz durch den Störabstand, gemessen in äquivalenter Energie Eb je Informationsbit bezogen auf die einseitige Rauschleistungsdichte N0, repräsentiert, der notwendig ist, um eine hinreichende Zuverlässigkeit der digitalen Übertragung zu erreichen (hier Bitfehlerrate BER 10 ). Die gestrichelten Kurven gelten für binäre, primitive BCH Codes (siehe z.B. [12]) mit Blocklänge 31 bzw. 255. Mit zunehmender Korrekturfähigkeit wird zwar der erforderliche Störabstand geringer, zugleich fällt jedoch die Bandbreitene zienz infolge der Übertragung von mehr Kontrollsymbolen (sinkende Coderate). Bei gleicher Bandbreitene zienz sind nur rel. geringe Gewinne (ca. 2 dB) mit langen Codes im Vergleich zu uncodierter Übertragung zu erzielen, während sich kurze Codes im Bereich gröÿerer Bandbreitene zienz ( 2) als völlig nutzlos erweisen. Aus diesem Grund hat im Jahr 1974 J.L. Massey vorgeschlagen [13], Kanalcodierung und Modulation als Einheit zu betrachten und gemeinsam zu optimieren, und damit die sog. codierte Modulation begründet. In den Jahren 1976/77 haben Ungerböck [16, 15] und Imai [10] unabhängig voneinander leistungsfähige Verfahren zur codierte Modulation vorgestellt. In beiden Ansätzen wird anstelle der Hammingdistanz die minimale Euklidische Distanz der Signalpunkte im Signalraum maximiert. Bandbreitene ziente digitale Übertragungsverfahren beruhen für 3 Hz verzugsweise auf digitaler Pulsamplituden Modulation (PAM) mit einer Basissignalkonstellationen A IR in D Dimensionen (D = 1: ASK; D = 2: PSK, QAM) und M := 2` Signalpunkten. Zentral ist das Konzept der Zuordnung von binären Adressvektoren xm = (x0m; x 1 m; : : : ; x ` 1 m ), xm 2 f0; 1g zu den 2 ` Signalpunkten am, m = 1; 2; : : : ;M , der Signalkonstellation A. Vorzugsweise wird diese durch fortgesetzte Partitionierung der Signalmenge festgelegt. Die am häu gsten verwendete Zuordnungsmethode maximiert die minimale Euklidische Distanz innerhalb der Teil-

Udo Wachsmann

Papers

Multilevel codes: theoretical concepts and practical design rules

Power and bandwidth efficient digital communication using turbo codes in multilevel codes

Multilevel coding: aspects from information theory

Codierte Modulation mittels Multilevel-Codes: Entwicklung und aktueller Stand der Forschung