Consider coded transmission over a binary-input symmetric memoryless channel. The channel decoder uses the noisy observations of the code symbols to reproduce the transmitted code symbols. Thus, it combines the information about individual code symbols to obtain an over-all information about each code symbol, which may be the reproduced code symbol or its a-posteriori probability. This tutorial addresses the problem of "information combining" from an information-theory point of view: the decoder combines the mutual information between channel input symbols and channel output symbols (observations) to the mutual information between one transmitted symbol and all channel output symbols. The actual value of the combined information depends on the statistical structure of the channels. However, it can be upper and lower bounded for the assumed class of channels. This book first introduces the concept of mutual information profiles and revisits the well-known Jensen's inequality. Using these tools, the bounds on information combining are derived for single parity-check codes and for repetition codes. The application of the bounds is illustrated in four examples: information processing characteristics of coding schemes, including extrinsic information transfer (EXIT) functions; design of multiple turbo codes; bounds for the decoding threshold of low-density parity-check codes; EXIT function of the accumulator.
{"title":"Information Combining","authors":"I. Land, J. Huber","doi":"10.1561/0100000013","DOIUrl":"https://doi.org/10.1561/0100000013","url":null,"abstract":"Consider coded transmission over a binary-input symmetric memoryless channel. The channel decoder uses the noisy observations of the code symbols to reproduce the transmitted code symbols. Thus, it combines the information about individual code symbols to obtain an over-all information about each code symbol, which may be the reproduced code symbol or its a-posteriori probability. This tutorial addresses the problem of \"information combining\" from an information-theory point of view: the decoder combines the mutual information between channel input symbols and channel output symbols (observations) to the mutual information between one transmitted symbol and all channel output symbols. The actual value of the combined information depends on the statistical structure of the channels. However, it can be upper and lower bounded for the assumed class of channels. This book first introduces the concept of mutual information profiles and revisits the well-known Jensen's inequality. Using these tools, the bounds on information combining are derived for single parity-check codes and for repetition codes. The application of the bounds is illustrated in four examples: information processing characteristics of coding schemes, including extrinsic information transfer (EXIT) functions; design of multiple turbo codes; bounds for the decoding threshold of low-density parity-check codes; EXIT function of the accumulator.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"537 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2006-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88166006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The control and reduction of multiuser interference is a fundamental problem in wireless communications. In order to increase the spectral efficiency and to provide individual quality-of-service (QoS), it is required to jointly optimize the power allocation together with possible receive and transmit strategies. This often leads to complex and difficult-to-handle problem formulations. There are many examples in the literature, where the special structure of the problem is exploited in order to solve special cases of this problem (e.g. multiuser beamforming or CDMA). So it is desirable to have a general theory, which can be applied to many practical QoS measures, like rates, delay, BER, etc. These measures can all be related to the signal-to-interference ratio (SIR) or the signal-to-interference-plus-noise ratio (SINR). This leads to the problem of SIR and SINR balancing, which is fundamental for many problems in communication theory.
{"title":"QoS-Based Resource Allocation and Transceiver Optimization","authors":"M. Schubert, H. Boche","doi":"10.1561/0100000010","DOIUrl":"https://doi.org/10.1561/0100000010","url":null,"abstract":"The control and reduction of multiuser interference is a fundamental problem in wireless communications. In order to increase the spectral efficiency and to provide individual quality-of-service (QoS), it is required to jointly optimize the power allocation together with possible receive and transmit strategies. This often leads to complex and difficult-to-handle problem formulations. There are many examples in the literature, where the special structure of the problem is exploited in order to solve special cases of this problem (e.g. multiuser beamforming or CDMA). So it is desirable to have a general theory, which can be applied to many practical QoS measures, like rates, delay, BER, etc. These measures can all be related to the signal-to-interference ratio (SIR) or the signal-to-interference-plus-noise ratio (SINR). This leads to the problem of SIR and SINR balancing, which is fundamental for many problems in communication theory.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2006-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76315643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is focused on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their performance without resorting to computer simulations. It also provides a benchmark for testing the sub-optimality of iterative (or other practical) decoding algorithms. This analysis also establishes the goodness of linear codes (or ensembles), determined by the gap between their achievable rates under optimal ML decoding and information theoretical limits. In this article, upper and lower bounds on the error probability of linear codes under ML decoding are surveyed and applied to codes and ensembles of codes on graphs. For upper bounds, we discuss various bounds where focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we address de Caen's based bounds and their improvements, and also consider sphere-packing bounds with their recent improvements targeting codes of moderate block lengths.
{"title":"Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial","authors":"I. Sason, S. Shamai","doi":"10.1561/0100000009","DOIUrl":"https://doi.org/10.1561/0100000009","url":null,"abstract":"This article is focused on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their performance without resorting to computer simulations. It also provides a benchmark for testing the sub-optimality of iterative (or other practical) decoding algorithms. This analysis also establishes the goodness of linear codes (or ensembles), determined by the gap between their achievable rates under optimal ML decoding and information theoretical limits. In this article, upper and lower bounds on the error probability of linear codes under ML decoding are surveyed and applied to codes and ensembles of codes on graphs. For upper bounds, we discuss various bounds where focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we address de Caen's based bounds and their improvements, and also consider sphere-packing bounds with their recent improvements targeting codes of moderate block lengths.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"61 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2006-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81490387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory.
{"title":"Network Coding Theory - Part II: Multiple Source","authors":"R. Yeung, S. Li, N. Cai, Zhen Zhang","doi":"10.1561/0100000007II","DOIUrl":"https://doi.org/10.1561/0100000007II","url":null,"abstract":"Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"37 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2005-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88441347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory.
{"title":"Network Coding Theory - Part I: Single Source","authors":"R. Yeung, S. Li, N. Cai, Zhen Zhang","doi":"10.1561/0100000007I","DOIUrl":"https://doi.org/10.1561/0100000007I","url":null,"abstract":"Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"260 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72876217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.
{"title":"Toeplitz and Circulant Matrices: A Review","authors":"R. Gray","doi":"10.1561/0100000006","DOIUrl":"https://doi.org/10.1561/0100000006","url":null,"abstract":"The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"30 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2005-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79276376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Geometric Programming (GP) is a class of nonlinear optimization with many useful theoretical and computational properties. Over the last few years, GP has been used to solve a variety of problems in the analysis and design of communication systems in several 'layers' in the communication network architecture, including information theory problems, signal processing algorithms, basic queuing system optimization, many network resource allocation problems such as power control and congestion control, and cross-layer design. We also start to understand why, in addition to how, GP can be applied to a surprisingly wide range of problems in communication systems. These applications have in turn spurred new research activities on GP, especially generalizations of GP formulations and development of distributed algorithms to solve GP in a network. This text provides both an in-depth tutorial on the theory, algorithms, and modeling methods of GP, and a comprehensive survey on the applications of GP to the study of communication systems.
{"title":"Geometric Programming for Communication Systems","authors":"M. Chiang","doi":"10.1561/0100000005","DOIUrl":"https://doi.org/10.1561/0100000005","url":null,"abstract":"Geometric Programming (GP) is a class of nonlinear optimization with many useful theoretical and computational properties. Over the last few years, GP has been used to solve a variety of problems in the analysis and design of communication systems in several 'layers' in the communication network architecture, including information theory problems, signal processing algorithms, basic queuing system optimization, many network resource allocation problems such as power control and congestion control, and cross-layer design. We also start to understand why, in addition to how, GP can be applied to a surprisingly wide range of problems in communication systems. These applications have in turn spurred new research activities on GP, especially generalizations of GP formulations and development of distributed algorithms to solve GP in a network. This text provides both an in-depth tutorial on the theory, algorithms, and modeling methods of GP, and a comprehensive survey on the applications of GP to the study of communication systems.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"41 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2005-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78973419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The information measure known as information divergence or Kullback-Leibler distance or relative entropy plays a key role, often with a geometric flavor as an analogue of squared Euclidean distance, as in the concepts of I-projection, I-radius and I-centroid. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory.
{"title":"Information Theory and Statistics: A Tutorial","authors":"I. Csiszár, P. Shields","doi":"10.1561/0100000004","DOIUrl":"https://doi.org/10.1561/0100000004","url":null,"abstract":"This tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The information measure known as information divergence or Kullback-Leibler distance or relative entropy plays a key role, often with a geometric flavor as an analogue of squared Euclidean distance, as in the concepts of I-projection, I-radius and I-centroid. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an \"information geometry\" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"23 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2004-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78168698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available.The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible to a large audience.
{"title":"Algebraic Number Theory and Code Design for Rayleigh Fading Channels","authors":"F. Oggier, E. Viterbo","doi":"10.1561/0100000003","DOIUrl":"https://doi.org/10.1561/0100000003","url":null,"abstract":"Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available.The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible to a large audience.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"277 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72573523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wireless communication system design was until recently thought to have been limited in practice by time and bandwidth. The discovery that space, obtained by increasing the number of transmit and receive antennas, can also effectively generate degrees of freedom, and hence expand the range of choices made available to the design offers system designers important new opportunities. This paper focuses on the main aspects of single-user multiple-antenna theory, with the goal of presenting a comprehensive, yet compact, survey, emphasizing its mathematical aspects. After describing channel models, we compute the capacities they achieve, we briefly overview "space-time" codes, and we describe how suboptimum architectures can be employed to simplify the receiver.
{"title":"Transmission and Reception with Multiple Antennas: Theoretical Foundations","authors":"E. Biglieri, G. Taricco","doi":"10.1561/0100000002","DOIUrl":"https://doi.org/10.1561/0100000002","url":null,"abstract":"Wireless communication system design was until recently thought to have been limited in practice by time and bandwidth. The discovery that space, obtained by increasing the number of transmit and receive antennas, can also effectively generate degrees of freedom, and hence expand the range of choices made available to the design offers system designers important new opportunities. This paper focuses on the main aspects of single-user multiple-antenna theory, with the goal of presenting a comprehensive, yet compact, survey, emphasizing its mathematical aspects. After describing channel models, we compute the capacities they achieve, we briefly overview \"space-time\" codes, and we describe how suboptimum architectures can be employed to simplify the receiver.","PeriodicalId":45236,"journal":{"name":"Foundations and Trends in Communications and Information Theory","volume":"41 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2004-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74844613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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