Coset codes. I. Introduction and geometrical classification
TL;DR: The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters.
Abstract: Practically all known good constructive coding techniques for bandlimited channels, including lattice codes and various trellis-coded modulation schemes, can be characterized as coset codes. A coset code is defined by a lattice partition Lambda / Lambda ' and by a binary encoder C that selects a sequence of cosets of the lattice Lambda '. The fundamental coding gain of a coset code, as well as other important parameters such as the error coefficient, the decoding complexity, and the constellation expansion factor, are purely geometric parameters determined by C Lambda / Lambda '. The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters. >
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Proceedings Article•
01 Jan 2005
TL;DR: This book aims to provide a chronology of key events and individuals involved in the development of microelectronics technology over the past 50 years and some of the individuals involved have been identified and named.
Abstract: Alhussein Abouzeid Rensselaer Polytechnic Institute Raviraj Adve University of Toronto Dharma Agrawal University of Cincinnati Walid Ahmed Tyco M/A-COM Sonia Aissa University of Quebec, INRSEMT Huseyin Arslan University of South Florida Nallanathan Arumugam National University of Singapore Saewoong Bahk Seoul National University Claus Bauer Dolby Laboratories Brahim Bensaou Hong Kong University of Science and Technology Rick Blum Lehigh University Michael Buehrer Virginia Tech Antonio Capone Politecnico di Milano Javier Gómez Castellanos National University of Mexico Claude Castelluccia INRIA Henry Chan The Hong Kong Polytechnic University Ajit Chaturvedi Indian Institute of Technology Kanpur Jyh-Cheng Chen National Tsing Hua University Yong Huat Chew Institute for Infocomm Research Tricia Chigan Michigan Tech Dong-Ho Cho Korea Advanced Institute of Science and Tech. Jinho Choi University of New South Wales Carlos Cordeiro Philips Research USA Laurie Cuthbert Queen Mary University of London Arek Dadej University of South Australia Sajal Das University of Texas at Arlington Franco Davoli DIST University of Genoa Xiaodai Dong, University of Alberta Hassan El-sallabi Helsinki University of Technology Ozgur Ercetin Sabanci University Elza Erkip Polytechnic University Romano Fantacci University of Florence Frank Fitzek Aalborg University Mario Freire University of Beira Interior Vincent Gaudet University of Alberta Jairo Gutierrez University of Auckland Michael Hadjitheodosiou University of Maryland Zhu Han University of Maryland College Park Christian Hartmann Technische Universitat Munchen Hossam Hassanein Queen's University Soong Boon Hee Nanyang Technological University Paul Ho Simon Fraser University Antonio Iera University "Mediterranea" of Reggio Calabria Markku Juntti University of Oulu Stefan Kaiser DoCoMo Euro-Labs Nei Kato Tohoku University Dongkyun Kim Kyungpook National University Ryuji Kohno Yokohama National University Bhaskar Krishnamachari University of Southern California Giridhar Krishnamurthy Indian Institute of Technology Madras Lutz Lampe University of British Columbia Bjorn Landfeldt The University of Sydney Peter Langendoerfer IHP Microelectronics Technologies Eddie Law Ryerson University in Toronto
7,826 citations
Cites background from "Coset codes. I. Introduction and ge..."
...Path loss exponents at higher frequencies tend to be higher [31, 26, 25, 27] while path loss exponents at higher antenna heights tend to be lower [34]....
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...The capacity of time-varying frequency-selective fading channels is in general unknown, however upper and lower bounds and limiting formulas exist [30, 31]....
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TL;DR: This paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed, and an adaptive-lattice trellis-coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the DMMT channel.
Abstract: Multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels. This paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed. A compact model is developed for the multiple-input multiple-output (MIMO) dispersive spatially selective wireless communication channel. The multivariate information capacity is analyzed. For high signal-to-noise ratio (SNR) conditions, the MIMO channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components, the number of input antennas, or the number of output antennas. This desirable result is contrasted with the lower capacity slope of the well-studied case with multiple antennas at only one side of the radio link. A spatio-temporal vector-coding (STVC) communication structure is suggested as a means for achieving MIMO channel capacity. The complexity of STVC motivates a more practical reduced-complexity discrete matrix multitone (DMMT) space-frequency coding approach. Both of these structures are shown to be asymptotically optimum. An adaptive-lattice trellis-coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the DMMT channel. Experimental examples that support the theoretical results are presented.
1,593 citations
TL;DR: A novel algorithm is developed that is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder and is supported by intuitive arguments and simulation results in many relevant scenarios.
Abstract: Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.
1,410 citations
Cites background from "Coset codes. I. Introduction and ge..."
...A lattice code (or constellation) is the set of lattice points , where is some shaping region [41], [42]....
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TL;DR: This work addresses the problem of compressing correlated distributed sources, i.e., correlated sources which are not co-located or which cannot cooperate to directly exploit their correlation and provides a constructive practical framework based on algebraic trellis codes dubbed as DIstributed Source Coding Using Syndromes (DISCUS), that can be applicable in a variety of settings.
Abstract: We address the problem of compressing correlated distributed sources, i.e., correlated sources which are not co-located or which cannot cooperate to directly exploit their correlation. We consider the related problem of compressing a source which is correlated with another source that is available only at the decoder. This problem has been studied in the information theory literature under the name of the Slepian-Wolf (1973) source coding problem for the lossless coding case, and as "rate-distortion with side information" for the lossy coding case. We provide a constructive practical framework based on algebraic trellis codes dubbed as DIstributed Source Coding Using Syndromes (DISCUS), that can be applicable in a variety of settings. Simulation results are presented for source coding of independent and identically distributed (i.i.d.) Gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded. Our results reveal the promise of this approach: using trellis-based quantization and coset construction, the performance of the proposed approach is 2-5 dB from the Wyner-Ziv (1976) bound.
1,060 citations
References
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Book•
01 Dec 1987
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Abstract: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics.
4,564 citations
IBM1
TL;DR: A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth by channel coding with expanded sets of multilevel/phase signals in a manner which increases free Euclidean distance.
Abstract: A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. This is achieved by channel coding with expanded sets of multilevel/phase signals in a manner which increases free Euclidean distance. Soft maximum--likelihood (ML) decoding using the Viterbi algorithm is assumed. Following a discussion of channel capacity, simple hand-designed trellis codes are presented for 8 phase-shift keying (PSK) and 16 quadrature amplitude-shift keying (QASK) modulation. These simple codes achieve coding gains in the order of 3-4 dB. It is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals, which we call "mapping by set partitioning." Based on a new distance measure between binary code sequences which efficiently lower-bounds the Euclidean distance between the corresponding channel signal sequences, a search procedure for more powerful codes is developed. Codes with coding gains up to 6 dB are obtained for a variety of multilevel/phase modulation schemes. Simulation results are presented and an example of carrier-phase tracking is discussed.
4,091 citations
IBM1
TL;DR: The effects of carrier-phase offset in carrier-modulated TCM systems are discussed, and recent advances in TCM schemes that use signal sets defined in more than two dimensions are described, and other work related to trellis-coded modulation is mentioned.
Abstract: I the,art in trellis-coded modulation (TCM) is given for the more interested reader. First, the general structure of TCM schemes and the principles of code construction are reviewed. Next, the effects of carrier-phase offset in carrier-modulated TCM systems are discussed. The topic i s important, since TCM schemes turn out to be more sensitive to phase offset than uncoded modulation systems. Also, TCM schemes are generally not phase invariant to the same extent as their signal sets. Finally, recent advances in TCM schemes that use signal sets defined in more than two dimensions are described, and other work related to trellis-coded modulation is mentioned. The best codes currently known for one-, two-, four-, and eight-dimensional signal sets are given in an Appendix. T h e trellis structure of the early hand-designed TCM schemes and the heuristic rules used to assign signals to trellis transitions suggested that TCM schemes should have an interpretation in terms of convolutional codes with a special signal mapping. This mapping should be based on grouping signals into subsets with large distance between the subset signals. Attempts to explain TCM schemes in this manner led to the general structure of TCM encoders/modulators depicted in Fig. 1. According to this figure, TCM signals are generated as follows: When m bits are to be transmitted per encoder/modulator operation, m 5 m bits are expanded by a rate-rYd(m-t 1) binary convolutional encoder into rii-t 1 coded bits. These bits are used to select one of 2' \" + I subsets of a redundant 2'11+1-ary signal set. The remaining mm uncoded bits determine which of the 2 \" '-' \" signals in this subset is to be transmitted. The concept of set partitioning is of central significance for TCM schemes. Figure 2 shows this concept for a 32-CROSS signal set [ 11, a signal set of lattice type \" Z2 \". Generally, the notation \" Zk \" is used to denote an infinite \" lattice \" of points in k-dimensional space with integer coordinates. Lattice-type signal sets are finite subsets of lattice points, which are centered around the origin and have a minimum spacing of A,. Set partitioning divides a signal set successively into smaller subsets with maximally increasing smallest two-way. The partitioning is repeated iii 4-1 times until A,,+, is equal to or greater than the desired free distance of the TCM scheme to be designed. T h e finally …
814 citations
TL;DR: Minimal encoders are shown to be immune to catastrophic error propagation and, in fact, to lead in a certain sense to the shortest decoded error sequences possible per error event.
Abstract: A convolutional encoder is defined as any constant linear sequential circuit. The associated code is the set of all output sequences resulting from any set of input sequences beginning at any time. Encoders are called equivalent if they generate the same code. The invariant factor theorem is used to determine when a convolutional encoder has a feedback-free inverse, and the minimum delay of any inverse. All encoders are shown to be equivalent to minimal encoders, which are feedback-free encoders with feedback-free delay-free inverses, and which can be realized in the conventional manner with as few memory elements as any equivalent encoder, Minimal encoders are shown to be immune to catastrophic error propagation and, in fact, to lead in a certain sense to the shortest decoded error sequences possible per error event. In two appendices, we introduce dual codes and syndromes, and show that a minimal encoder for a dual code has exactly the complexity of the original encoder; we show that systematic encoders with feedback form a canonical class, and compare this class to the minimal class.
801 citations
TL;DR: This paper attempts to present a comprehensive tutorial survey of the development of efficient modulation techniques for bandlimited channels, such as telephone channels, with principal emphasis on coded modulation techniques, in which there is an explosion of current interest.
Abstract: This paper attempts to present a comprehensive tutorial survey of the development of efficient modulation techniques for bandlimited channels, such as telephone channels. After a history of advances in commercial high-speed modems and a discussion of theoretical limits, it reviews efforts to optimize two-dimensional signal constellations and presents further elaborations of uncoded modulation. Its principal emphasis, however, is on coded modulation techniques, in which there is an explosion of current interest, both for research and for practical application. Both block-coded and trellis-coded modulation are covered, in a common framework. A few new techniques are presented.
770 citations