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Multilevel Codes: Theoretical Concepts and Practical Design Rules
, 1999
"... This paper deals with 2 ` 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 ..."
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Cited by 207 (33 self)
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This paper deals with 2 ` 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 maximumlikelihood 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, dimensional...
Coset codes–Part I: Introduction and geometrical classification
 IEEE Transactions on Information Theory
, 1988
"... AbstractPractically all known good constructive coding techniques for ..."
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Cited by 44 (0 self)
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AbstractPractically all known good constructive coding techniques for
The Cell Structures of Certain Lattices
, 1991
"... . The most important lattices in Euclidean space of dimension n 8 are the lattices A n (n ³ 2), D n (n ³ 4), E n (n = 6 , 7 , 8) and their duals. In this paper we determine the cell structures of all these lattices and their Voronoi and Delaunay polytopes in a uniform manner. The results for E 6 * ..."
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Cited by 24 (6 self)
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. The most important lattices in Euclidean space of dimension n 8 are the lattices A n (n ³ 2), D n (n ³ 4), E n (n = 6 , 7 , 8) and their duals. In this paper we determine the cell structures of all these lattices and their Voronoi and Delaunay polytopes in a uniform manner. The results for E 6 * and E 7 * simplify recent work of Worley, and also provide what may be new spacefilling polytopes in dimensions 6 and 7. 1. Introduction The CoxeterDynkin diagrams of types A n , D n , E 6 , E 7 and E 8 arise in surprisingly different parts of mathematics  see the discussions by Arnold [1] and Hazewinkel et al. [30]. In the present paper we study __________________ * This paper appeared in {\m Miscellanea mathematica}, P. Hilton, F. Hirzebruch, and R. Remmert, Eds., SpringerVerlag, NY, 1991, pp. 71107. (**) From the English version AutodaFe(Continuum, New York, p. 385) as translated by C. V. Wedgwood: "You have but to know an object by its proper name for it to lose its dange...
Coded Modulation by MultilevelCodes: Overview and State of the Art
, 1998
"... The development of theory for multilevel coding during the last 20 years is reminded. Several design rules are compared and the capacity region of multilevel codes is outlined. We discuss the dimensionality of the constituent signal constellation and compare different labeling strategies by means of ..."
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Cited by 10 (2 self)
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The development of theory for multilevel coding during the last 20 years is reminded. Several design rules are compared and the capacity region of multilevel codes is outlined. We discuss the dimensionality of the constituent signal constellation and compare different labeling strategies by means of random coding exponent. Finally, by discussing bit interleaved coded modulation we show that the progress in theory now leads back to the origin of coded modulation. 1 Introduction and Historical Overview During the first 25 years after the foundation of information theory by C.E. Shannon 50 years ago research in channel coding was almost entirely restricted to coding for binary antipodal signalling like BPSK, QPSK with Gray mapping etc. It soon was recognized that a direct application of traditional forward error correcting codes (FEC) to bandwidth efficient modulation schemes with more than two signal points per dimension of a signal space, e.g. M ? 2ary ASK, M ? 4ary QAM, M ? 4ar...
Lineartime nearest point algorithms for Coxeter lattices
, 2009
"... The Coxeter lattices, which we denote An/m, are a family of lattices containing many of the important lattices in low dimensions. This includes An, E7, E8 and their duals A ∗ n, E ∗ 7 and E ∗ 8. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, ..."
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Cited by 4 (2 self)
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The Coxeter lattices, which we denote An/m, are a family of lattices containing many of the important lattices in low dimensions. This includes An, E7, E8 and their duals A ∗ n, E ∗ 7 and E ∗ 8. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexity O(n log n) and the other with worst case complexity O(n) where n is the dimension of the lattice. We show that for the particular lattices An and A ∗ n the algorithms reduce to simple nearest point algorithms that already exist in the literature.
Error Control Techniques for Satellite and Space Communications NASA Grant Number NAG5557 Principal Investigator:
, 1990
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Principal Investigator:
, 1986
"... following areas: 1) Undetected Error Probability and Throughput Analysis of a Concatenated Coding Scheme. A paper summarizing our work on the performance analysis of NASA's telecommand system has been accepted for publication by the IEEE Transactions on Communications [ 11. Copies of this pap ..."
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following areas: 1) Undetected Error Probability and Throughput Analysis of a Concatenated Coding Scheme. A paper summarizing our work on the performance analysis of NASA's telecommand system has been accepted for publication by the IEEE Transactions on Communications [ 11. Copies of this paper were included in a previous report. 2) Capacity and Cutoff Rate Analysis of Concatenated Codes. A paper summarizing our work on analyzing the capacity and cutoff rate of the &quot;outer channel &quot; formed by the combination of the actual physical channel and the inner encoder and decoder in a NASA concatenated coding system has been accepted for publication by the IEEE Transactions on Information Theory [2]. Copies of this paper were included in a previous report. 3) Concatenated Codes Using Bandwidth Efficient Trellis Inner Codes. A paper summarizing our work on determining the performance of bandwidth efficient trellis inner codes for use in a NASA concatenated coding system is being prepared for submission to the IEEE Transactions on Communications [3]. A presen