Trellis-coded multidimensional phase modulation
TL;DR: A systematic approach to partitioning L*MPSK signal sets that is based on block coding is used and an encoder system approach is developed that incorporates the design of a differential precoder, a systematic convolutional encoder, and a signal set mapper.
Abstract: A 2L-dimensional multiple phase-shift keyed (L*MPSK) signal set is obtained by forming the Cartesian product of L two-dimensional MPSK signal sets. A systematic approach to partitioning L*MPSK signal sets that is based on block coding is used. An encoder system approach is developed. It incorporates the design of a differential precoder, a systematic convolutional encoder, and a signal set mapper. Trellis-coded L*4PSK, L*8PSK, and L*16PSK modulation schemes are found for 1 >
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Book•
23 Nov 2007
TL;DR: This new edition now contains essential information on steganalysis and steganography, and digital watermark embedding is given a complete update with new processes and applications.
Abstract: Digital audio, video, images, and documents are flying through cyberspace to their respective owners. Unfortunately, along the way, individuals may choose to intervene and take this content for themselves. Digital watermarking and steganography technology greatly reduces the instances of this by limiting or eliminating the ability of third parties to decipher the content that he has taken. The many techiniques of digital watermarking (embedding a code) and steganography (hiding information) continue to evolve as applications that necessitate them do the same. The authors of this second edition provide an update on the framework for applying these techniques that they provided researchers and professionals in the first well-received edition. Steganography and steganalysis (the art of detecting hidden information) have been added to a robust treatment of digital watermarking, as many in each field research and deal with the other. New material includes watermarking with side information, QIM, and dirty-paper codes. The revision and inclusion of new material by these influential authors has created a must-own book for anyone in this profession.
*This new edition now contains essential information on steganalysis and steganography
*New concepts and new applications including QIM introduced
*Digital watermark embedding is given a complete update with new processes and applications
1,773 citations
TL;DR: This paper deals with 2/sup l/-ary transmission using multilevel coding (MLC) and multistage decoding (MSD) and shows that capacity can in fact be closely approached at high bandwidth efficiencies.
Abstract: 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.
1,030 citations
TL;DR: This paper surveys how the capacity of the linear Gaussian channel has been met during the past half century, and new capacity-approaching techniques include turbo coding and decoding, multilevel coding, and combined coding/precoding for intersymbol-interference channels.
Abstract: Shannon's determination of the capacity of the linear Gaussian channel has posed a magnificent challenge to succeeding generations of researchers. This paper surveys how this challenge has been met during the past half century. Orthogonal minimum-bandwidth modulation techniques and channel capacity are discussed. Binary coding techniques for low-signal-to-noise ratio (SNR) channels and nonbinary coding techniques for high-SNR channels are reviewed. Recent developments, which now allow capacity to be approached on any linear Gaussian channel, are surveyed. These new capacity-approaching techniques include turbo coding and decoding, multilevel coding, and combined coding/precoding for intersymbol-interference channels.
675 citations
Cites background or methods from "Trellis-coded multidimensional phas..."
...Such codes are given for QAM in [105], [113], , and for -PSK in [87], [114], ; ....
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...In [87], principles of set partitioning of multidimensional -PSK constellations are given, based on concepts of multilevel block coding; tables of linear -PSK trellis codes are presented for and with the largest degree of rotational invariance given for each code; and figures similar to Fig....
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TL;DR: A bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes and is very powerful, yet of modest complexity since simple component codes are used.
Abstract: We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used.
529 citations
Cites background or methods from "Trellis-coded multidimensional phas..."
...Multidimensional TCM allows even higher bandwidth efficiency than traditional Ungerboeck TCM by assigning more than one symbol per trellis transition or step [10]....
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...In the Appendix, we have derived the symbol-by-symbol MAP decoder for nonbinary trellises....
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Book•
09 Sep 2002
TL;DR: This paper presents a Comparative Study of Turbo Equalisers: The Super Trellis Structure of Convolutional Turbo Codes and the Coded Modulation Theory and Performance.
Abstract: Acknowledgments.Historical Perspective, Motivation and Outline. I Convolutional and Block Coding. Convolutional Channel Coding. Block Coding. Soft Decoding and Performance of BCH Codes. II Turbo Convolutional and Turbo Block Coding. Turbo Convolutional Coding. The Super Trellis Structure of Convolutional Turbo Codes. Turbo BCH Coding. Redundant Residue Number System Codes. III Coded Modulation: TCM, TTCM, BICM, BICM ID. Coded Modulation Theory and Performance. IV Space Time Block and Space Time Trellis Coding. Space time Block Codes. Space Time Trellis Codes. Turbo coded Adaptive QAM versus Space time Trellis Coding. V Turbo Equalisation. Turbo coded Partial response Modulation. Turbo Equalisation for Partial response Systems. Turbo Equalisation Performance Bound. Comparative Study of Turbo Equalisers. Reduced complexity Turbo Equaliser. Turbo Equalisation for Space time Trellis coded Systems. Summary and Conclusions. Bibliography. Subject Index. Author Index. About the Authors.Other Related Wiley and IEEE Press Books.
407 citations
References
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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
TL;DR: A new multilevel coding method that uses several error-correcting codes that makes effective use of soft-decisions to improve the performance of decoding and is superior to other multileVEL coding systems.
Abstract: A new multilevel coding method that uses several error-correcting codes is proposed. The transmission symbols are constructed by combining symbols of codewords of these codes. Usually, these codes are binary error-correcting codes and have different error-correcting capabilities. For various channels, efficient systems can be obtained by choosing these codes appropriately. Encoding and decoding procedures for this method are relatively simple compared with those of other multilevel coding methods. In addition, this method makes effective use of soft-decisions to improve the performance of decoding. The decoding error probability is analyzed for multiphase modulation, and numerical comparisons to other multilevel coding systems are made. When equally complex systems are compared, the new system is superior to other multilevel coding systems.
1,070 citations
IBM1
TL;DR: An introduction into TCM is given, reasons for the development of TCM are reviewed, and examples of simple TCM schemes are discussed.
Abstract: rellis-Coded Modulation (TCM) has evolved over the past decade as a combined coding and modulation technique for digital transmission over band-limited channels. Its main attraction comes from the fact that it allows the achievement of significant coding gains over conventional uncoded multilevel modulation without compromising bandwidth efficiency. T h e first TCM schemes were proposed in 1976 [I]. Following a more detailed publication [2] in 1982, an explosion of research and actual implementations of TCM took place, to the point where today there is a good understanding of the theory and capabilities of TCM methods. In Part 1 of this two-part article, an introduction into TCM is given. T h e reasons for the development of TCM are reviewed, and examples of simple TCM schemes are discussed. Part I1 [I51 provides further insight into code design and performance, and addresses. recent advances in TCM. TCM schemes employ redundant nonbinary modulation in combination with a finite-state encoder which governs the selection of modulation signals to generate coded signal sequences. In the receiver, the noisy signals are decoded by a soft-decision maximum-likelihood sequence decoder. Simple four-state TCM schemes can improve. the robustness of digital transmission against additive noise by 3 dB, compared to conventional , uncoded modulation. With more complex TCM schemes, the coding gain can reach 6 dB or more. These gains are obtained without bandwidth expansion or reduction of the effective information rate as required by traditional error-correction schemes. Shannon's information theory predicted the existence of coded modulation schemes with these characteristics more than three decades ago. T h e development of effective TCM techniques and today's signal-processing technology now allow these ,gains to be obtained in practice. Signal waveforms representing information sequences ~ are most impervious to noise-induced detection errors if they are very different from each other. Mathematically, this translates into therequirement that signal sequences should have large distance in Euclidean signal space. ~ T h e essential new concept of TCM that led to the afore-1 mentioned gains was to use signal-set expansion to I provide redundancy for coding, and to design coding and ' signal-mapping functions jointly so as to maximize ~ directly the \" free distance \" (minimum Euclidean distance) between coded signal sequences. This allowed the construction of modulation codes whose free distance significantly exceeded the minimum distance between uncoded modulation signals, at the same information rate, bandwidth, and signal power. The term \" …
874 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: 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