Optimization of signal sets for partial-response channels. II.Asymptotic coding gain

For Pt. I see ibid., vol.37, no.5, p.1327-141 (1991). For a linear, time-invariant, discrete-time channel with a given transfer function H(f), and information rate R bits/ T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2^RK inputs of length K that maximizes the minimum l₂ distance between pairs of outputs. The author studies the minimum distance between outputs, or equivalently, the coding gain of optimal signal sets as K→∞. He shows how to estimate the coding gain, relative to single-step detection, of an optimal signal set length K when K is large     

Coding techniques for partial-response channels

A coding technique for improving the reliability of digital transmission over noisy partial-response channels with characteristics (±D^m), m=1, 2, where the channel input symbols are constrained to be ±1, is presented. In particular, the application of a traditional modulation code as an inner code of a concentrated coding scheme in which the outer code is designed for maximum (free) Hamming distance is considered. A performance comparison is made between the concentrated scheme and a coding technique presented by Wolf and G. Ungerboeck (see ibid., vol. COM-34, p.765-773, Aug. 1986) for the dicode channel with transfer function (1- D)     

Improved coding techniques for preceded partial-response channels

A coset of a convolutional code may be used to generate a zero-run length limited trellis code for a 1-D partial-response channel. The free squared Euclidean distance, d_free², at the channel output is lower bounded by the free Hamming distance of the convolutional code. The lower bound suggests the use of a convolutional code with maximal free Hamming distance, d_max(R,N), for given rate R and number of decoder states N. In this paper we present cosets of convolutional codes that generate trellis codes with d_free ²>d_max(R,N) for rates 1/5⩽R⩽7/9 and (d _free²=d_max(R,N) for R=13/16,29/32,61/64, The tabulated convolutional codes with R⩽7/9 were not optimized for Hamming distance. Instead, a computer search was used to determine cosets of convolutional codes that exploit the memory of the 1-D channel to increase d_free² at the channel output. The search was limited by only considering cosets with certain structural properties. The R⩾13/16 codes were obtained using a new construction technique for convolutional codes with free Hamming distance 4. Newly developed bounds on the maximum zero-run lengths of cosets were used to ensure a short maximum run length at the 1-D channel output     

Iterative reduced-search decoding for coded partial-response channels

The full-complexity soft-input/soft-output (SISO) detector based on the BCJR algorithm for coded partial-response channels has a computational complexity growing exponentially with channel memory length. In this letter, we propose a low complexity soft-output channel detector based on the Chase decoding algorithm, which was previously applied to decode turbo product codes. At each iteration, the proposed detector forms a candidate list using all possible combinations of bit patterns in the weakest indices based on tentative hard estimates and a priori information fed back from the outer decoder. To demonstrate the performance/complexity tradeoff of the proposed detector, simulation results over rate-8/9 turbo-coded EPR4 and ME/sup 2/PR4 channels are presented, respectively. It is shown that the proposed detector can significantly reduce the computational complexity with only a small performance loss compared to the BCJR algorithm.     

Sequence estimation for class-IV partial-response channels withjitter

An analysis is presented of the output of class-IV partial-response channels corrupted simultaneously by jitter and additive white noise. The authors analyze the behavior of the least-squares (LS) decoder for this channel. They introduce the projection-minimization (P-M) algorithm and demonstrate that, under favorable conditions, its performance, even when not acceptable on its own, could possibly be beneficial when used in conjunction with the LS decoder in enhancing the reliability of the channel. Implementation of the P-M decoder is rather expensive, and it is not at all clear that combining the P-M algorithm with LS decoding and traditional error control schemes is the best way of dealing with channels corrupted by jitter. It may be possible to avoid the P-M algorithm and instead utilize a more aggressive traditional error correction scheme. Alternatively, it may be possible to choose modulation schemes which utilize pulses whose derivatives at the sampled values are small, and perhaps obtain better results than with partial-response class-IV signaling     

Precoding technique for partial-response channels with applicationsto HDTV transmission

An equivalent partial-response (PR) channel 1-Z^-k arises in the envisioned terrestrial over-the-air broadcasting of digital high-definition television (HDTV) signals when a comb filter is used by an HDTV receiver to reduce the NTSC cochannel interference. The design of signal constellations and their associated precoders for this PR channel is considered. Besides PAM and square QAM, it is shown that generalized square and hexagonal constellations can also be used. Coded modulation and graceful degradation in the received signal quality are discussed. The results extended to a more general PR channel     

A 50 MHz eight-tap adaptive equalizer for partial-response channels

A new architecture for digital implementation of the adaptive equalizer in Class IV partial-response maximum likelihood (PRML) channels employing parallelism and pipelining is described. The architecture was used in a prototype integrated circuit in a 1.2 μm CMOS technology to implement an eight-tap adaptive equalizer and Viterbi sequence detector which consumes a total of 70 mW from a 3.3 V supply operating at an input sampling rate of 50 MHz     

Constrained block codes for class-IV partial-response channels withmaximum-likelihood sequence estimation

Significant improvements in magnetic storage densities have been made feasible by the application of partial-response signaling combined with maximum-likelihood sequence estimation. To enhance the performance of this technique when applied to the class-IV partial-response channel, which is recognized as being appropriate to model the magnetic recording channel, it is often required to bound the number of consecutive zeros in the recorded data sequence and its odd and even subsequences. We investigate block codes that satisfy such a constraint. In particular, we look for a set of maximal number of fixed-length sequences such that any pair of them can be concatenated without violating the constraint. In many cases, depending on the constraint and the length of the sequences, we determine such a set, and in the remaining cases, we determine at most three candidates for it. These results are used to study the best possible constrained block codes     

Kikuchi approximation method for joint decoding of LDPC codes and partial-response channels

In this letter, we apply the Kikuchi approximation method to the problem of joint decoding of a low-density parity-check code and a partial-response channel. The Kikuchi method is, in general, more powerful than the conventional loopy belief propagation (BP) algorithm, and can produce better approximations to an underlying inference problem. We will first review the Kikuchi approximation method and the generalized BP algorithm, which is an iterative message-passing algorithm based on this method. We will then report simulation results which show that the Kikuchi method outperforms the best conventional iterative method.     

Optimization of nonlinear signal constellations for real-world MIMO channels

The performance of spatial multiplexing (SM) multiple-input multiple-output (MIMO) communication systems is highly dependent on the richness of scattering, the presence of dominant components, and the interelement spacings. In this paper, a new interpretation of the impact of transmit correlation on the performance of SM is given based on a so-called "symbol-related array factor." Nonlinear signal constellations for SM over real-world fading channels are then designed by minimizing an estimate of the average symbol error rate under an average transmit power constraint. The new transmission scheme exploits the spectral efficiency advantage of SM and the robustness of eigen-beamforming. Through simulations, it is shown to be more robust against fading correlations and high Ricean K-factors than SM using the classical phase shift keying (PSK) and quadrature amplitude modulation (QAM) constellations. The symbol error rate performance of this scheme is not affected by a change in the propagation environment or the interelement distance. Furthermore, if the scheme is used on the uplink, no explicit rate-consuming feedback link from the base station to the mobile station is required.     

Multidimensional signal sets through the shell construction forparallel channels

The authors derive a procedure to send r bits on M parallel channels. A decomposition of the best constellation in Z^M+(1/2, . . ., 1/2) is given in terms of the cross-products of lower dimensional shells of points. The proposed scheme can be used with good known coset codes to provide an alternate method of coded modulation. The results indicate that one can get good shaping gains for low encoder complexity. The method is also generalized for channels with unequal gains. The authors also find a significant performance advantage at fixed shaping gain, in certain cases, with respect to the recent Voronoi constellations in terms of peak-to-average power and constellation expansion     

Efficient signal processing techniques for exploiting transmitantenna diversity on fading channels

A class of powerful and computationally efficient strategies for exploiting transmit antenna diversity on fading channels is developed. These strategies, which require simple linear processing at the transmitter and receiver, have attractive asymptotic characteristics. In particular, given a sufficient number of transmit antennas, these techniques effectively transform a nonselective Rayleigh fading channel into a nonfading, simple white marginally Gaussian noise channel with no intersymbol interference. These strategies, which we refer to as linear antenna precoding, can be efficiently combined with trellis coding and other popular error-correcting codes for bandwidth-constrained Gaussian channels. Linear antenna precoding requires no additional power or bandwidth and is attractive in terms of robustness and delay considerations. The resulting schemes have powerful and convenient interpretations in terms of transforming nonselective fading channels into frequency- and time-selective ones     

Numerical optimization techniques applied to PPM signal design

A computer-oriented algorithm is developed for designing optimum waveforms for a pulse-position-modulation communication system. Nonlinear modulation threshold effects are incorporated directly into the design by introducing constraints on the sidelobe peaks of the autocorrelation function. The search is performed over the class of signals satisfying constraints on average power, peak power, and bandwidth. The optimum signal in this class is the one whose autocorrelation function has the sharpest central peak while the sidelobe peaks are below the specified constraint level. Numerical results for a realistic problem are presented, and the effect of introducing the correlation and peak power constraints is studied. It is shown that a large reduction in the sidelobe peaks is possible with relatively little loss in the sharpness of the central peak.     

Performance evaluation of low-density parity-check codes on partial-response channels using density evolution

A method to evaluate the performance of a low-density parity-check (LDPC) code on partial-response (PR) channels in terms of the noise threshold and decoding error is presented. Given a particular codeword or assuming an independent and uniformly distributed (i.u.d.) codeword for transmission, the density-evolution algorithm is used to compute the probability density function of messages passing in the decoding process, from which the decoding error is extracted. This estimated i.u.d. decoding error is used to approximate the decoding error of an ensemble of LDPC codes on arbitrary PR channels. Comparison with simulation results shows that it is a very good approximation for the simulated codes, provided their length is large enough.     

Blind equalization of turbo trellis-coded partial-response continuous-phase modulation signaling over narrow-band Rician fading channels

In this paper, a blind maximum-likelihood channel estimation algorithm is developed for turbo trellis-coded/continuous-phase modulation (TTC/CPM) signals propagating through additive white Gaussian noise (AWGN) and Rician fading environments. We present CPM for TTC signals, since it provides low spectral occupancy and is suitable for power- and bandwidth-limited channels. Here, the Baum-Welch (BW) algorithm is modified to estimate the channel parameters. We investigate the performance of TTC/CPM for 16-CPFSK over AWGN and Rician channels for different frame sizes, in the case of ideal channel state information (CSI), no CSI, and BW estimated CSI.     

Performance of component interleaved signal sets for fadingchannels

The authors calculate the exact (pairwise) error probability for an arbitrary component-interleaved 2-D constellation over the Rayleigh fading channel. Using this result, they improve the accuracy of the performance analysis at high error rates. For illustration, this is applied to signal sets derived from 4-PSK and 16-QAM over the Rayleigh fading channel     

Time-varying techniques for multisensor signal detection

In source detection and localization, the presence of a common but unknown signal can be detected from several noisy sensor measurements using the generalized coherence (GC) estimate. We propose to improve the performance of the GC estimate for multisensor detection using noise-suppressed signal estimates obtained from time-varying techniques. If one of the sensors has a significantly higher signal-to-noise ratio (SNR) than the other sensors, then it could be preprocessed prior to the GC estimate to improve detection performance for the remaining, lower SNR sensors. We perform this processing by estimating time-varying signals of interest with nonlinear phase functions using two methods: a) a modified matching pursuit decomposition (MMPD) algorithm whose dictionary is similar, in time-frequency structure, to the signal and b) an instantaneous frequency (IF) estimation method using highly localized time-frequency representations. The MMPD can yield signal estimates with lower mean square errors than the IF estimation technique but at the expense of higher computational cost and memory requirements. Using simulations, we compare the performance of the GC estimate with the significantly improved performance of the GC estimate that employs the signal estimate from the high SNR sensor. For the two-sensor detection, the estimated signal is also used with a generalized likelihood ratio test statistic to further improve performance.     

Second-order statistics for diversity-combining techniques inNakagami-fading channels

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for the M branch pure selection combining (PSC), equal gain combining (EGC), and maximal ratio combining (MRC), techniques, assuming independent branches in a Nakagami (1960) environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The model developed here is general and can be easily applied to other fading statistics (e.g., Rice)