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Journal ArticleDOI

Multistage decoding of multilevel block M-PSK modulation codes and its performance analysis

TL;DR: The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity.
Abstract: Multistage decoding of multilevel block multilevel phase-shift keying (M-PSK) modulation codes for the additive white Gaussian noise (AWGN) channel is investigated. Several types of multistage decoding, including a suboptimum soft-decision decoding scheme, are devised and analyzed. Upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes. Error probabilities of some specific multilevel block 8-PSK modulation codes are evaluated and simulated. The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity. In one example, it is shown that the difference in performance between the proposed suboptimum multistage soft-decision decoding and the single-stage optimum decoding is small, only a fraction of a dB loss in SNR at the block error probability of 10/sup -6/. >
Citations
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Journal ArticleDOI
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


Cites background or methods from "Multistage decoding of multilevel b..."

  • ...• Upper bounds on the word-error probability of modulation schemes based on binary lattices and-ary PSK constellations, respectively, with MLC where overall maximum-likelihood decoding and MSD are considered [83] and [52]....

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  • ..., [48], [26], [27], [51], and [52]), the balanced distances rule was used for rate design although multistage decoding was applied....

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Journal ArticleDOI
01 Sep 1995
TL;DR: A straightforward derivation of iterative Turbo decoding and the concept of extrinsic information is presented and 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.
Abstract: 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.

119 citations

Journal ArticleDOI
TL;DR: The authors present coded 8-phase-shift-keyed (8-PSK) modulations for the Rayleigh fading channel and a suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated.
Abstract: The authors present coded 8-phase-shift-keyed (8-PSK) modulations for the Rayleigh fading channel. The schemes are based on multilevel trellis-coded-modulation constructions and utilize maximum free Hamming distance binary convolutional codes as building blocks. A suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated. Examples are constructed to show that the proposed schemes outperform the best modified codes of the Ungerboeck type due to significantly higher implicit time diversity, yielding seven branches of built-in time diversity, whereas the Ungerboeck code yields four branches of time diversity for a 64-state system. The transmission delay is higher, however. The new schemes can provide three levels of unequal error protection when 8-PSK or 8-differential-phase-shift-keying (8-DPSK) modulations are used. They provide 10-14-dB channel signal-to-noise ratio gain over uncoded 4-DPSK at a bit error rate of 10/sup -3/ for a modest decoding complexity. >

95 citations

Journal ArticleDOI
TL;DR: The error performance of some of these codes based on both one-stage optimum decoding and multistage suboptimum decoding has been simulated and show that these codes achieve good error performance with small decoding complexity.
Abstract: The multilevel coding technique is used for constructing multilevel trellis M-ary phase-shift-keying (MPSK) modulation codes for the Rayleigh fading channel. In the construction of a code, all the factors which affect the code performance and its decoding complexity are considered. The error performance of some of these codes based on both one-stage optimum decoding and multistage suboptimum decoding has been simulated. The simulation results show that these codes achieve good error performance with small decoding complexity. >

40 citations

Journal ArticleDOI
TL;DR: Three noncoherent block coded twisted amplitude and phase shift keying schemes which are derived from non coherent block-coded MPSK are proposed and NBC-8TAPSK has the best bit error performance among allnoncoherent schemes.
Abstract: For coherent detection, block-coded modulation is a bandwidth efficient scheme. In this paper, we propose theorems about the error performance of block-coded modulation using M-ary phase-shift keying (MPSK) for noncoherent detection. Based on these theorems, we propose a novel block-coded modulation scheme for noncoherent detection called noncoherent block-coded MPSK. The proposed scheme provides flexible designs of noncoherent block codes with different code rate, block length and error performance. Good noncoherent block codes can be easily obtained by properly choosing binary linear block codes as the component codes. Moreover, noncoherent block codes of this new scheme can be decoded by multistage decoding, which has the advantage of low complexity and satisfactory error performance. In this paper, two algorithms of multistage decoding for noncoherent detection are proposed as well. The error performance of some designed codes and decoding algorithms is verified by computer simulation.

31 citations


Cites background or methods from "Multistage decoding of multilevel b..."

  • ...Fortunately, BCM can be easily decoded by a suboptimal decoding called multistage decoding which is accomplished by decoding the component codes one at a time [ 12 ]....

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  • ...Therefore, we propose two algorithms of multistage decoding [ 12 ] for NBC-MPSK....

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References
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Book
01 Jan 1977
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Abstract: Linear Codes. Nonlinear Codes, Hadamard Matrices, Designs and the Golay Code. An Introduction to BCH Codes and Finite Fields. Finite Fields. Dual Codes and Their Weight Distribution. Codes, Designs and Perfect Codes. Cyclic Codes. Cyclic Codes: Idempotents and Mattson-Solomon Polynomials. BCH Codes. Reed-Solomon and Justesen Codes. MDS Codes. Alternant, Goppa and Other Generalized BCH Codes. Reed-Muller Codes. First-Order Reed-Muller Codes. Second-Order Reed-Muller, Kerdock and Preparata Codes. Quadratic-Residue Codes. Bounds on the Size of a Code. Methods for Combining Codes. Self-dual Codes and Invariant Theory. The Golay Codes. Association Schemes. Appendix A. Tables of the Best Codes Known. Appendix B. Finite Geometries. Bibliography. Index.

10,083 citations

Journal ArticleDOI
G. Ungerboeck1
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

Journal ArticleDOI
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.
Abstract: In many cases an optimum or computationally convenient test of a simple hypothesis $H_0$ against a simple alternative $H_1$ may be given in the following form. Reject $H_0$ if $S_n = \sum^n_{j=1} X_j \leqq k,$ where $X_1, X_2, \cdots, X_n$ are $n$ independent observations of a chance variable $X$ whose distribution depends on the true hypothesis and where $k$ is some appropriate number. In particular the likelihood ratio test for fixed sample size can be reduced to this form. It is shown that with each test of the above form there is associated an index $\rho$. If $\rho_1$ and $\rho_2$ are the indices corresponding to two alternative tests $e = \log \rho_1/\log \rho_2$ measures the relative efficiency of these tests in the following sense. For large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample of size $en$ with the second test. To obtain the above result, use is made of the fact that $P(S_n \leqq na)$ behaves roughly like $m^n$ where $m$ is the minimum value assumed by the moment generating function of $X - a$. It is shown that if $H_0$ and $H_1$ specify probability distributions of $X$ which are very close to each other, one may approximate $\rho$ by assuming that $X$ is normally distributed.

3,760 citations

Journal ArticleDOI
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

Journal ArticleDOI
G. Ungerboeck1
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