By Topic

Selected Areas in Communications, IEEE Journal on

Issue 6 • Date Aug. 1989

Filter Results

Displaying Results 1 - 13 of 13
  • An algorithm for computing the distance spectrum of trellis codes

    Page(s): 929 - 940
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1178 KB)  

    A class of quasiregular codesis defined for which the distance spectrum can be calculated from the codeword corresponding to the all-zero information sequence. Convolutional codes and regular codes are both quasiregular, as well as most of the best known trellis codes. An algorithm to compute the distance spectrum of linear, regular, and quasiregular trellis codes is presented. In particular, it can calculate the weight spectrum of convolutional (linear trellis) codes and the distance spectrum of most of the best known trellis codes. The codes do not have to be linear or regular, and the signals do not have to be used with equal probabilities. The algorithm is derived from a bidirectional stack algorithm, although it could also be based on the Viterbi algorithm. The algorithm is used to calculate the beginning of the distance spectrum of some of the best known trellis codes and to compute tight estimates on the first-event-error probability and on the bit-error probability.<> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Closest coset decoding of |u|u+v| codes

    Page(s): 982 - 988
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB)  

    The general concept of closest coset decoding (CCD) is presented, and a soft-decoding technique for block codes that is based on partitioning a code into a subcode and its cosets is described. The computational complexity of the CCD algorithm is significantly less than that required if a maximum-likelihood detector (MLD) is used. A set-partitioning procedure and details of the CCD algorithm for soft decoding of |u|u+v| codes are presented. Upper bounds on the bit-error-rate (BER) performance of the proposed algorithm are combined, and numerical results and computer simulation tests for the BER performance of second-order Reed-Muller codes of length 16 and 32 are presented. The algorithm is a suboptimum decoding scheme and, in the range of signal-to-noise-power-density ratios of interest, its BER performance is only a few tenths of a dB inferior to the performance of the MLD for the codes examined View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Block coset codes for M-ary phase shift keying

    Page(s): 900 - 913
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1180 KB)  

    Construction of efficient block-encoded M-ary phase-shift-keying (M-PSK) schemes is investigated. An algebraic approach is adopted in which the basic modulation signals are associated with the elements of a finite group. Using some of the properties of group partition chains, the algebraic properties of the linear codes are studied. From this analysis, a class of codes called blocked coset codes is obtained. Distance properties of the block coset codes are obtained in terms of the distance properties of the underlying group partition chain. A particular choice of coset representations yields the standard block coset code construction, which is applicable to M-PSK for M of the form 2k×3l . The standard block coset code construction is seen to be equivalent to block code constructions previously reported in the literature, and it is modified to account for the fact that the 4-PSK constellation forms a Hamming space. The modification results in substantial improvements in some cases. A table of some examples of 2 k×3l PSK block coset codes is included View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations

    Page(s): 877 - 892
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1584 KB)  

    The authors discuss the major attributes desired in signal constellations, such as signal-to-noise ratio (SNR) efficiency, simplicity of mapping bits to points and vice versa, compatibility with coded modulation schemes, and compatibility with quadrature amplitude modulation (QAM). The capability of supporting a so-called opportunistic secondary channel, often used for internal control signaling, is considered. The gain in SNR efficiency of a multidimensional constellation (lattice code) consisting of the points from a lattice Λ within a region R compared to a cubic constellation is shown to be approximately separable into the coding gain of Λ and the shape gain of R, for large constellations. Similarly, the expansion of the associated constituent 2-D constellation is shown to be approximately separable into a constellation expansion ratio (CER) coding component CERc(Λ) and a shaping component CER s(R). The N sphere is the region R with the best shape gain, but N also has large constellation expansion. Bounds for the best possible shape gain versus CERs(R) or peak-to-average-power ratio (PAR) are given. Generalized cross constellations are discussed. These constellations yield a modest shape gain with very low CERs(R) or PAR, are easily implemented, are well suited for use with coded QAM modems, and can be readily adapted to support an opportunistic secondary channel View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Reduced-state sequence estimation for coded modulation of intersymbol interference channels

    Page(s): 989 - 995
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (708 KB)  

    The authors investigated the detection of trellis codes designed for channels that are intersymbol interference free when they operate in the presence of intersymbol interference. A well-structured reduced-state sequence estimation (RSSE) algorithm is described which can achieve the performance of maximum-likelihood sequence estimation (MLSE) with drastically reduced complexity. Well-defined reduced-state trellises are first constructed by merging the states of the ML supertrellis using set partitioning principles. Then the Viterbi algorithm is used to search these trellises. A special case of RSSE, called parallel decision-feedback decoding, uses the encoder trellis, yet on channels with large attenuation distortion it can provide a significantly better performance than linear equalization. The performance of RSSE is examined analytically and through simulation, and then compared to that of MLSE and ideal decision-feedback equalization. It is noted that the performance advantage of RSSE can be obtained without significantly increasing the decoding delay or complicating an adaptive implementation View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Multidimensional constellations. II. Voronoi constellations

    Page(s): 941 - 958
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1772 KB)  

    For pt.I see ibid., vol.7, no.6, p.877-92 (1989). Voronoi constellations, also called Voronoi codes are implementable N-dimensional constellations based on partitions of N-dimensional lattices (Λ) that can achieve good shape gains and that are inherently suited for use with coded modulation. Two methods are given for specifying Voronoi constellations on the basis of arbitrary lattice partitions Λ/Λs, where Λs, the shaping lattice, is an N-dimensional sublattice of Λ. One of the methods is conjectured to be optimum, and the other has desirable symmetries and naturally supports opportunistic secondary channels. When Λ and Λs are 2-D-symmetric, the constituent 2-D constellation is itself a Voronoi constellation. The shaping constellation expansion ratio and peak-to-average-power ratio are determined in general and for various Λs. Methods for labeling Voronoi constellations are given. Their complexity is shown to be dominated by that of decoding Λs. It is also shown that coding and shaping are separable and dual. Bounds on the shape gain of Voronoi constellations are given that depend on the depth and normalized informativity of Λs. These bounds suggest the use of lattices Λ with depth 2 and normalized informativity less than 1, which can achieve near-optimal shape gains with reduced constellation expansion and implementation complexity View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Some optimal codes have structure

    Page(s): 893 - 899
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (556 KB)  

    The techniques of the geometry of numbers, especially the Minkowski-Hlawka theorem, are used to modify Shannon's existence proof for optimal channel codes, so that the modified proof applies specifically to lattice codes. The resulting existence proof states that there exist lattice codes which satisfy Shannon's bound to within the factor 4, and hence match the reliability exponent and critical rate bounds which Shannon derived for optimal codes with unspecified structure. Therefore, it is demonstrated that optimal codes need not be random, but rather that some of them have structure, e.g. the structure of a lattice code View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Decoding of severely filtered modulation codes using the (M, L) algorithm

    Page(s): 1006 - 1016
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (740 KB)  

    The problem of decoding data in the presence of infinite-duration intersymbol interference that is caused by severe channel filtering is considered. Filtered continuous phase modulations (CPM) are the particular object of study. A state-variable approach is used for defining the decoder tree. Maximum likelihood sequence estimation requires exhaustive tree searching, which is restricted by using the ( M, L) algorithm since this approach does not require that the channel intersymbol interference be finite. After briefly describing the (M, L) algorithm, the authors motivate the problem of equalization of infinite-impulse-response channels by considering the performance of a discrete-time single-pole channel filtering a binary input sequence. The state variable description of a linear system is used to analyze the filtered modulation. The state of the filtered modulation for a given input modulation is used to define the tree structure of the filtered signal upon which the (M, L) algorithm operates. The minimum signal space distance results for several filtered CPM schemes are then summarized. Extensive simulation results are presented, and comparisons to the optimal performance are made View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A two-stage sequential demodulator for the Gosset lattice

    Page(s): 974 - 981
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (692 KB)  

    A construction of the Gosset lattice is considered that has practical advantages over other constructions of the same lattice. Codes derived from this construction have been shown to exhibit a null at DC in their baseband spectrum. A two-stage approach to the demodulation of this construction of the Gosset lattice is discussed. This demodulator consists of an initial stage which may declare erasures and a secondary stage designed to correct erasures. A study of erasure events is made and then used to reduce the number of steps in the second-stage correction algorithm. While the overall demodulator is somewhat more complex than a straight forward maximum-likelihood demodulator designed for this construction, the present structure has the advantage of greater speed View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Wide-band digital subscriber access with multidimensional block modulation and decision-feedback equalization

    Page(s): 996 - 1005
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (860 KB)  

    The author investigates the potential transmission performance of pair-wire subscriber lines at the higher rate of 800 kb/s, with particular reference to digital subscriber line transmission for ISDN (integrated services digital network) basic access. Block modulation schemes of 1-4 dimensions, at a rate of 2 bits per dimension, are considered. Time-division multiplexing is used to combine the multiple dimensions for transmission over a single-waveform channel, namely, the subscriber line. The channel noise is assumed to be additive and dominated by near-end crosstalk. MMSE (minimum mean-squared error) decision-feedback equalization is used to deal with the noise and the intersymbol interference. Using the theory developed, the potential performance of some simple lines is calculated. The coding gain of a multidimensional modulation scheme is found to be fully preserved after transmission if the equalizer is infinite in length. However, the gain realized can be much lower, or none at all, if the equalizer is only moderate in length. This latter phenomenon is due to the fact that the noise at the decision point is coloured, due to the inability of the equalizer to whiten it sufficiently View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Baseband line codes via spectral factorization

    Page(s): 914 - 928
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1044 KB)  

    A description is given of a methodology for designing baseband line codes with prescribed spectral nulls in the transmitted spectrum. These codes have the property that the transmitted power is adjustable (with a concomitant change in spectral shape, i.e. null width) and can be made arbitrarily close to the innovations power, while keeping the minimum distance between signal points (or sequences) constant. The essential design step requires the spectral factorization of a certain trigonometric polynomial. The line code that results can easily be used in conjunction with a large class of trellis-coded modulation schemes. Specific baseband codes are constructed using a representation of the general theory that involves a dither variable, which is used to create integer symbols and to minimize the size of the symbol alphabet. Emphasis is on the design of line codes with a double null at DC using the symbol alphabet {±1, ±3} View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A Leech lattice modem

    Page(s): 968 - 973
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (588 KB)  

    A 24-dimensional block code based on the Leech lattice is described for use in a 19200-b/s modem. Encoding (the process of converting binary data into message point coordinates) and detection (conversion of the received coordinates into the coordinates of the nearest code point of the lattice) are described. Decoding (the further conversion of these into binary data) is not described, since it consists of an easily achieved reversal of the encoding process. Block (1000-bit-length) error rates in the presence of white noise for baud rates of 2400 and 2743, the two baud rates at which the modem can operate, are presented. Encoding plus decoding was successfully programmed for an ADSP2100 signal processor requiring altogether slightly less than one half the processing capability View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Fast decoding of the Leech lattice

    Page(s): 959 - 967
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (700 KB)  

    An efficient algorithm is presented for maximum-likelihood soft-decision decoding of the Leech lattice. The superiority of this decoder with respect to both computational and memory complexities is demonstrated in comparison with previously published decoding methods. Gain factors in the range of 2-10 are achieved. The authors conclude with some more advanced ideas for achieving a further reduction of the algorithm complexity based on a generalization of the Wagner decoding method to two parity constraints. A comparison with the complexity of some trellis-coded modulation schemes is discussed. The decoding algorithm presented seems to achieve a computational complexity comparable to that of the equivalent trellis codes View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.

Aims & Scope

IEEE Journal on Selected Areas in Communications focuses on all telecommunications, including telephone, telegraphy, facsimile, and point-to-point television, by electromagnetic propagation.

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Muriel Médard
MIT