Fetal movement counting can provide valuable information on the fetal health, as a strong decrease in the number of movements can be seen as a precursor to fetal death. Typically, assessment of fetal health by fetal movement counting relies on the maternal perception of fetal activity. The percentage of detected movements is strongly subject dependent and with undivided attention of the mother varies between 37% and 88%. Various methods to assist in fetal movement detection exist based on a wide spectrum of measurement techniques. However, these are unsuitable for ambulatory or long-term observation. In this paper, a novel low-complexity method for fetal movement detection is presented based on amplitude and shape changes in the abdominally recorded fetal ECG. This method was compared to a state-of-the-art method from the literature. Using ultrasound-based movement annotations as ground truth, the presented method outperforms the state-of-the-art abdominal-ECG based method, with a sensitivity, specificity, and accuracy of 56%, 68%, and 63%, respectively. Additionally, a significant reduction in algorithm complexity is achieved, possibly enabling continuous ambulatory fetal movement detection and early detection of reduced fetal motility.

This work provides a feasibility study on estimating the 3-D locations of several thousand miniaturized free-floating sensor platforms. The localization is performed on basis of sparse ultrasound range measurements between sensor platforms and without the use of beacons.

In a multimode transceiver, the transmitter for one communication standard induces a large interference on the receiver for another one. When this large interference passes through the inherently nonlinear receiver Front-End (FE), it introduces Cross- Modulation (CM) distortion. Increasing the FE linearity to lower the CM distortion leads to unacceptable power consumption for a handheld device. Considering the continuous increase of digital computation power governed by Moore's law an attractive alternative approach is to digitally compensate for the CM distortion. An existing CM compensation method is tailored to single-mode transceivers and requires an auxiliary FE. By using the locally available transmitted interference in the multimode transceiver, we propose a CM compensation method which requires no additional analog hardware. Hence the power consumption and complexity of the multimode transceiver will be reduced significantly.

In multimode transceivers, the transmitter for one communication standard may induce a large interferer in the receiver for another standard. To linearly suppress this interferer, which can be several orders of magnitude larger than the desired received signal, the receiver should have a very large linear dynamic range, resulting in excessive power consumption. Many of potential interferers have a constant modulus modulation. Baier and Friederichs introduced a tuneable nonlinear circuit which can suppress a constant modulus interferer without excessive power consumption. Since an open- loop tuning method is used, the worst- case interference suppression was strongly limited by inaccuracy of circuit components. To alleviate this limitation, we propose a closed- loop tuning method that exploits the locally available interference as side information. Our analysis shows that the proposed method can strongly suppress the interferer while a symbol error rate performance close to that of an exactly linear receiver is achieved. Simulation results for a practical scenario confirm this analysis, and promise much smaller power consumption than for linear interference suppression approaches.

In this paper, we study carrier frequency offset (CFO) estimation in the uplink of multiuser offset QAM filter bank multicarrier (FBMC) communication systems. A low-complexity frequency-domain CFO estimator using periodical training sequences is proposed. We derive the theoretical mean square error (MSE) for the proposed estimator and computer simulations show that the derived MSE matches the simulated MSE closely. Compared with state-of-the- art time-domain estimators, the proposed estimator achieves better performance with a much lower computational complexity.

In a multimode transceiver, several communication standards may be active at the same time. Owing to the small size of the transceiver, the transmitter for one standard induces a large interference on the receiver for another one. When this large interference passes through the inherently non-linear receiver front-end (FE), distortion products are generated. Among these products, the cross-modulation (CM) product is the most problematic one, as it always has the same centre frequency as the desired signal. Increasing the FE linearity to lower the CM distortion leads to unacceptable power consumption for a handheld device. Considering the continuous increase of digital computation power governed by Moore's law an attractive alternative approach is to digitally compensate for the CM distortion. An existing solution to compensate for the CM distortion is tailored to single-mode transceivers and requires an auxiliary FE. By using the locally available transmitted interference in the multimode transceiver, the authors propose a CM compensation method which requires no additional analogue hardware. Hence the power consumption and complexity of the multimode transceiver can be reduced significantly. The simulation results demonstrate that the proposed method can lower distortion to a negligible amount at realistic interference levels.

We consider illumination sensing in a light emitting diode (LED) lighting system based on frequency division multiplexing (FDM). In the FDM scheme, LEDs render periodical illumination pulses at different frequencies with prescribed duty cycles. The purpose of illumination sensing is to identify the illumination contributions of different LEDs at a target location, within a limited response time. With the use of a photosensor at the target location, the problem of interest is to estimate the amplitude of the sensor signal component due to each LED. In this paper, we propose a successive estimation approach exploiting higher order harmonics of the sensor signal. We show that a larger number of LEDs can be supported using the proposed approach, as compared to our previous approach using only the fundamental frequency component, at the same estimation error.

This paper presents an analysis of the effect of carrier frequency offset (CFO) on offset QAM (OQAM) multicarrier filter bank (MCFB) systems, also known as staggered modulated multitone (SMT), over frequency-selective channels. This effect may be quantified by signal-to-interference ratio (SIR). We drive an accurate expression for the interference power and the desired signal power. Then SIR of SMT systems is calculated. Next, we drive an approximated SIR when the maximum delay of the channel is small in comparison with symbol spacing. The approximated SIR show that the SIR over frequency-selective channels converges to that over additive white Gaussian noise (AWGN) channels. Numerical results show that with increasing number of subcarriers, both of accurate and approximated forms of SIR as a function of CFO over frequency-selective channels converge to that over AWGN channels. Also, we compare SMT and orthogonal frequency division multiplexing (OFDM). It is shown that OFDM has better SIR in small CFO over frequency-selective channels. But with large number of subcarriers or high CFO, SMT outperforms OFDM.

In this work, we consider illumination sensing in a light emitting diode (LED) based illumination system that normally consists of a large number of LEDs. Illumination sensing is used in order to facilitate the control of such system whose complexity, due to the large number of LEDs, can be quite high. In this paper, key requirements, i.e. accuracy and speed, on illumination sensing are described. Furthermore, we present a filter bank sensor structure based on frequency division multiplexing. The design of the filter response is discussed in the context of supporting maximum number of LEDs, while the key requirements on illumination sensing are satisfied. In particular, it is shown that, through the use of the filter with a triangular filter response, a large number of LEDs can be supported in the presence of frequency offsets in a practical range.

In the uplink of multi-user multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems, there are multiple carrier frequency offsets (CFO's) from the multiple users. In this paper, we study algorithms to estimate these multiple CFO values. We first derive the maximum likelihood (ML) estimator and show that the complexity of the ML estimator increases exponentially with the number of users so that the estimator is not suitable for practical implementations. To reduce the complexity, we propose a sub-optimal algorithm using constant amplitude zero autocorrelation (CAZAC) sequences. The complexity of the proposed method increases only linearly with the number of users. Using computer simulations, we compare the performance using CAZAC training sequences with that using the m sequence and the short training field (STF) of the IEEE 802.11n systems. The results show that in the low to medium SNR regions, the performance using CAZAC sequences is very close to the single-user Cramer-Rao bound. For high SNR regions, an error floor exists due to multiple access interference (MAI). The error floor using CAZAC sequences is more than 10 times smaller compared to the error floor using the other two sequences.

We present Nyquist pulse shaping conditions for two- dimensional (2-D) digital communication systems to be free from inter-symbol interference, for general regular sampling grids. We provide examples of 2-D pulse functions satisfying these Nyquist conditions. In particular, we show that a family of 2-D pulse functions that we construct as separable pulse functions from one-dimensional Nyquist-1 pulse functions obey the 2-D Nyquist criterion and moreover include the one with minimum support area in the frequency domain.

Media noise is the dominant noise that severely degrades the channel detector's performance for high-density optical recording. In this paper, we first propose a simple but general channel model for rewritable optical recording systems with media noise. We further develop various detection approaches to combat media noise. In particular, two novel modifications to the channel detector are proposed: i) monic constrained minimum mean square error (MMSE) based equalization with media noise considerations, and ii) a modified Viterbi detector (VD) accounting for data-dependent noise variance. The proposed modifications provide significant performance gain over the conventional detection approaches that are designed for additive, white and Gaussian noise (AWGN), without increasing the size of the VD trellis. Furthermore, a new constrained parity-check (PC) code and a data-dependent post-processing scheme are proposed based on the modified detection approaches. Simulation results show that compared to the system designed without considering media noise and without PC codes, the proposed scheme achieves an overall performance gain of more than 11 dB at high media noise levels.

Combining orthogonal frequency division multiplexing (OFDM) and multiple input and multiple output (MIMO) technologies enables high spectral efficiency data transmission over frequency selective fading channels. However, carrier frequency offset (CFO) and channel estimation become more complex for MIMO-OFDM systems. In this paper, we propose a class of efficient shift-orthogonal training sequences to assist joint CFO and channel estimation. We show that with the proposed training sequence, the CFO estimation touches Cramer- Rao bound (CRB) at practical SNR values. Such sequences are efficient as the overhead used for channel estimation can be significantly reduced compared to using conventional training sequence designs. We also derive a tight lower bound on the MSE of the channel estimation in the presence of the residual CFO.

In Liu and Toreli (1998), a blind carrier frequency offset (CFO) estimation method was proposed for orthogonal frequency multiplexing (OFDM) systems. This method makes use of the fact that in practical OFDM systems, there are some subcarriers that do not carry any data. However, the computation complexity of the method is rather high. In this paper, based on practical considerations, we propose a low complexity blind CFO estimation method. We derive an approximate closed-form solution for the CFO estimate. We show that the proposed algorithm achieves similar performance as the method in Liu and Toreli (1998) with significantly reduced computational complexity. For relatively large CFO values, we show that we could use the iterative algorithm in Wu et al. (2005) to improve the performance of the proposed algorithm.

The presence of residual carrier frequency offset (CFO) in an orthogonal frequency division multiplexing (OFDM) system leads to a loss of orthogonality between the subcarriers. This introduces inter-subcarrier interference and degrades the system performance significantly. In the literature, Liu and Tureli proposed a blind CFO estimation method based on the observation that in a typical OFDM system not all the subcarriers are used for data transmission. However, the computational complexity of such a method is very high. Based on practical considerations, we propose an approximate closed-form solution for the blind estimation of CFO that is easily implementable at a very low cost. We also propose a successive CFO estimation and compensation procedure, which reduces the performance degradation of the proposed algorithm as compared with the method of Liu and Tureli when relatively large CFO values are assumed. In addition, a decision-directed extension of the successive algorithm, which further improves the CFO estimation at a slightly higher complexity, is also given.

Receivers for partial response maximum-likelihood systems typically use a linear equalizer followed by a Viterbi detector. The equalizer tries to confine the channel intersymbol interference to a short span in order to limit the implementation complexity of the Viterbi detector. Equalization is usually made adaptive in order to compensate for channel variations. Conventional adaptation techniques, e.g., LMS, are, in general, suboptimal in terms of bit-error rate (BER). In this paper, we present a new equalizer adaptation algorithm that seeks to minimize the BER at the Viterbi detector output. The algorithm extracts information from the sequenced amplitude margin (SAM) histogram and incorporates a selection mechanism that focuses adaptation on particular data and noise realizations. The selection mechanism is based on the reliability of the add compare select (ACS) operations in the Viterbi detector. From a complexity standpoint, the algorithm is essentially as simple as the conventional LMS algorithm. Moreover, we present a further simplified version of the algorithm that does not require any hardware multiplications. Simulation results, for an idealized optical storage channel, confirm a substantial performance improvement relative to existing adaptation algorithms.

In high-density recording systems performance is largely determined by noise, n general different noise sources are present, where each source has direct impact on the overall performance. Therefore the characterization of a noise source provides insightful information about the recording system. In general noise characterization involves the choice of an appropriate stochastic model for it and furthermore the estimation of the parameters of the selected stochastic model. The characterization results can be used as diagnostic information to evaluate existing recording systems and they play an important role in state of the art bit-detection techniques. In these techniques the estimated stochastic parameters are used as side information to improve the detection reliability. For this reason an accurate estimation is very important. The estimation algorithm proposed in this paper, achieves a high estimation accuracy for systems where both data-dependent media noise and correlated additive noise are present. This algorithm makes use of the difference in data-dependency between the two noise sources to jointly estimate the stochastic parameters of the two noise sources.

In order to reduce the implementation complexity of maximum likelihood sequence detectors (MLSD), equalized maximum likelihood receivers are often used. This consists of employing an equalizer to transform the channel response to a short target response to which the Viterbi detector is matched. Existing equalizer and target adaptation schemes are often based on the minimum mean-square error (MMSE) criterion which is not always optimal in terms of detection bit-error rate at the Viterbi detector output. In this paper we consider minimum bit-error rate joint adaptation of equalizer and target response and present a practical adaptation algorithm that achieves near minimum bit-error rate performance. Our new equalizer and target adaptation scheme shows significant performance improvements in the presence of channel nonlinearities and media noise when compared to MMSE adaptation schemes. This is very promising for high density recording systems that are mainly hampered by media noise and channel nonlinearities. Moreover, from a complexity standpoint, the proposed algorithm is comparable to the MMSE-based algorithms.

A blind carrier frequency offset (CFO) estimation algorithm using the null subcarriers for orthogonal frequency diversity multiplexing (OFDM) systems was proposed in [1]. The optimal null subcarrier placement that minimizes the Cramer Rao bound (CRB) was studied in [3]. In this paper, we study the optimal null subcarrier placement from an SNR maximization point of view. We first derive the relationship between the SNR of the CFO estimation and the placement of null subcarriers. Based on that, we formulate the optimization problem and find the optimal solution using convex optimization for small CFO values. We also discuss the optimality of the null subcarrier placement in practical OFDM systems where guard bands are required at both ends of the spectrum.

In this paper a channel model is proposed for two-dimensional digital data storage systems. This channel model describes both the intersymbol interference structure and the noise structure. This noise structure is modelled as the output of a two-dimensional data-dependent autoregressive filter. The proposed model is simple, accurate and it is able to track channel variations. An experimental two-dimensional optical system is used to validate the proposed model and to illustrate the characterization process based on the model

Data receivers for storage systems normally operate at a fixed sampling rate 1/TSthat is asynchronous to the baud rate 1/T. A sampling-rate converter (SRC) serves to convert the incoming signal from the asynchronous to the synchronous clock domain. These receivers also contain an equalizer that serves to suppress intersymbol interference and noise. To limit receiver complexity, equalization burden can be shifted towards the SRC. This possibility is not exploited in any existing SRC. This paper presents SRC design methods that combine group delay flatness and out-of-band rejection criteria with the minimum mean square error equalization criterion. Numerical examples for an idealized optical recording channel validate the design methods

In this paper the cancellation of linear Intersymbol Interference (ISI) in two-dimensional systems is discussed. A theory is developed for the error rate of receivers that use tentative decisions to cancel ISI. Furthermore, precise conditions are formulated under which such ISI cancellation can be applied effectively. For many two-dimensional systems these conditions are easily met and therefore the application of ISI cancellation is of significant interest for these systems. The theory and the conditions are validated by simulation results for a two-dimensional channel model. Furthermore, results for an experimental two-dimensional optical storage system show that for a single layer disc with a capacity of 50 GB a substantial performance improvement may be obtained by applying ISI cancellation.

In this paper, we investigate various frequency-domain channel estimators for orthogonal frequency division multiplexing (OFDM) systems with virtual carriers (VCs). As conventional estimators cannot estimate the channel transfer function (CTF) at VCs, DFT-based estimators are not directly applicable in OFDM systems with VCs. To circumvent this, we present least squares (LS), generalized linear minimum mean square error (GLMMSE) and generalized singular value decomposition (GSVD) methods to estimate the CTF at VCs. Further, by exploiting the received data samples at VCs, we describe a novel noise variance estimation method. We also analyze the performance degradation due to estimated noise variance and the channel correlation mismatch. Performance comparison shows that the discrete Fourier transform (DFT)-based channel estimators incorporating the proposed CTF estimation at VCs achieve at least 6 dB gain when MMSE= 10-3 compared to frequency-domain LS estimator. Further, even though the DFT-based LS estimator with VCs performs worst among all the DFT-based estimators, it is the most robust estimator.

Receivers for partial response maximum-likelihood systems typically use a linear equalizer followed by a Viterbi detector. The equalizer tries to confine the channel intersymbol interference to a short span in order to limit the implementation complexity of the Viterbi detector. Equalization is usually made adaptive in order to compensate for channel variations. Conventional adaptation techniques, e.g. LMS, are in general suboptimal in terms of bit-error rate. In this paper we present a new equalizer adaptation algorithm that seeks to minimize bit-error rate at the Viterbi detector output. The algorithm extracts information from the sequenced amplitude margin (SAM) histogram and incorporates a selection mechanism that focuses adaptation on particular data and noise realizations. From a complexity standpoint, the algorithm is as simple as the conventional LMS algorithm. Simulation results, for an idealized optical storage channel, confirm a substantial performance improvement relative to existing adaptation algorithms

With storage capacities increasing much faster than data rates, fast read-out of content is becoming a bottleneck for the convenient use of optical storage devices. Two-dimensional optical storage (TwoDOS) is a new concept that solves this data-rate problem by using a multi-spot parallel readout system. In addition, the storage capacity is increased with a factor of at least 2. Using the same read-out physics as in the Blu-ray disc standard, single layered 12 cm discs with capacities up to 50 GB have been read out successfully at bit-rates as high as 560 Mbit/s. Basic pillars of TwoDOS are advanced signal processing and disc mastering techniques, and a proper design of the optical path.

Zero-forcing equalizer adaptation schemes are attractive because of their simplicity. We study their steady-state solution, and find that it is more poorly conditioned than that of least mean-square adaptation schemes. A simple yet effective solution to this problem, based on tap leakage, is proposed, analyzed, and exemplified for an idealized digital optical storage system.

The paper introduces the concept of two-dimensional optical storage (TwoDOS). In this concept, bits are written in a broad spiral consisting of a number of bit-rows stacked together in a hexagonal packing. Bits with a value '1' are represented physically as circular pit-holes on the disc, while bits with a value '0' are characterized by the absence of such a pit-hole. A scalar diffraction model is used to calculate the signal levels for various diameters of the pits. A stripe-wise Viterbi detector is proposed to perform 2D bit-detection with a limited state complexity of the trellis. Simulation results are shown for various diameters of the pits. A 2D modulation code is applied to eliminate patterns that yield a high probability of erroneous detection.

We derive performance bounds on bit error rates and error event probabilities for optical recording channels with d = 1 constraint. The bounds account for the use of various parity codes. They serve as benchmarks for the development of parity codes and post-processing schemes. Computer simulations have been carried out to demonstrate the accuracy of the proposed bounds and to evaluate the performance of various parity codes.

Asymmetry, also known as domain bloom, is a systematic imperfection caused by the writing process in optical or magneto-optical recording. At the reading end of the system, asymmetry causes shifts of adjacent signal transitions in opposite directions. We present a simple nonlinear model for the replay signal in the presence of asymmetry. The model is specified by a single parameter, which is proportional to asymmetry, and its accuracy is demonstrated by application to replay signals from digital video disk drives. Based on the proposed model, a maximum-likelihood sequence detector is designed for replay signals with asymmetry. Simple modifications of the proposed detector lead to significant reductions in complexity, while the attainable performance, evaluated both analytically and through error-rate simulations, is superior to that of conventional techniques.

Random channel errors that may occur in the run-length limited (RLL) channel bit-stream after bit-detection, are commonly repaired by error correction (de)coding (ECC) after demodulation of the RLL bitstream. RLL parity-check coding makes it possible to correct random errors already at the level of the channel bit-stream, at a much lower overhead than needed for standard ECC. With parity-check coding, a certain parity-check constraint is realized on segments of the RLL channel bit-stream. Violation of the parity-check constraint in the as-detected RLL bit-stream enables error detection; for error correction, some side information from the channel waveform is needed. One scheme from the literature considers parsing of parity-check blocks into the original RLL bit-stream. Another scheme is concatenated parity-check coding. While the parsing scheme has the drawback of low coding efficiency, its advantage is its simplicity and the lack of error propagation. The concatenated scheme has a high efficiency but it suffers from error propagation, and local demodulation is needed to derive the parity checks. As an alternative solution, we propose to use a parity-check coding scheme based on a combination of codes. Such a scheme is called 'combi-code', a term that was proposed within the framework of DC-free RLL codes. Apart from a main RLL code, a second RLL code, the parity-check enabling code, is required. The latter code is used to set the parity-check constraint of a segment to a predetermined value. Parity-check coding via combi-codes combines the advantages of the two other schemes: simplicity, a high coding efficiency, and no error propagation.

A modified E3PRML (ME3PRML) channel with concatenated coding is proposed for d=1 coded magnetic recording channels. First an analytical approach to obtain the optimized target is detailed, and compared with that obtained by search. It is observed that the channel is dominated by single bit error events. A concatenated code with interleaving in conjunction with the 2/3 (1,7) code, and a low-complexity correction method are proposed to detect and correct the dominant error events. For a code rate of 300/459 with 6-way interleaving, the proposed channel provides an improvement of 1.5 dB (including code rate loss) over conventional d=1 E3PRML channel at a bit-error rate of 1E-5, and better robustness to non-linearities than d=0 ME2PRML channel.

This study is concerned with the development of a simple yet sufficiently accurate model for the replay signal in optical discs. A method is proposed which models data storage (the write channel) as a nonlinear process and data retrieval (the read channel) as a linear one. The result is a low-complexity nonlinear model, of which the linear binary-PAM model is a special case. The performance of the proposed model is demonstrated by application to experimentally measured DVD data, and is found to be both accurate as well as robust to different recording media and conditions.

Besides timing recovery and automatic gain control, data receivers often perform adaptive slope or bandwidth control. This note presents a set of maximum run-length constraints that facilitates the joint accomplishment of these three tasks. Simple polarity-bit codes that introduce these constraints are described. The study is of particular interest in digital magnetic recording.

Quadra-phase (QP) is a binary modulation code with desirable features for use in digital magnetic recording. The paper describes simple data-aided timing acquisition and tracking techniques for QP that do not involve any oversampling and automatically achieve word synchronization.>

This paper develops a class of data-aided timing-recovery schemes whose structure and operating principle are reminiscent of zero-forcing equalizer adaptation. The schemes exhibit no pattern-dependent jitter and are applicable to a variety of modulation codes and reception techniques. They come in both oversampled and baud-rate forms, and permit maximum-likelihood tracking performance whenever the oversampling factor satisfies the sampling theorem. Subject to this condition, even simple schemes can be close to optimum. It is shown that various existing; schemes belong to the class under study or are closely related to it.>

This paper assesses the tracking capabilities of data-aided timing recovery schemes in terms of an efficiency that characterizes, coarsely speaking, the amount of timing information that the scheme manages to extract from the incoming signal per unit of time and signal-to-noise ratio. Efficiencies of maximum-likelihood and various baud-rate timing recovery schemes are determined as a function of the data and channel parameters, and are optimized with respect to design freedoms of the schemes. These results are illustrated for partial-response channels and idealized digital recording channels.>

is well known that the performance of a data receiver for an intersymbol interference (ISI) channel can depend strongly on the detection delay δ. For a discrete-time communication system, this paper derives a lower bound on the bit-error probability as a function of δ. This “restricted delay bound” is governed by a “restricted-delay distance” d(δ). In many instances, it improves upon Forney’s bound, which is governed by the minimum distance dmin. For instance, for partial-response channels, d(δ) does not converge to dmineven as δ-∝. For channels without spectral zeros, a finite detection delay suffices for d(δ) to coincide with dmin. For all finite δ, d(δ) is determined by a finite number of error patterns and may be computed in a straightforward manner. Unlike dmin, d(δ) depends on the phase characteristics of the channel. Minimum phase is proved to maximize d(δ). The lower bound is generalized to discrete-time channels with colored noise and to continuous-time channels. The effect of transforming a continuous-time channel into a discrete-time channel is discussed. Transformation via a matched filter, as in the IS1 canceller and a Viterbi detector due to Ungerboeck and MacKechnie, is shown to result in poor restricted-delay properties. Implications of these results are illustrated by means of examples.

For a digital recording system with a binary modulation encoder and a linearly dispersive channel with additive noise, the author determines optimum mean-square performance of the linear, partial-response, and decision-feedback equalizers. The analysis revolves around the power spectral density A( Omega ) of the code and the folded signal-to-noise ratio X( Omega ) of the channel. The latter function is analyzed for stylized optical and magnetic recording channels. For all equalizers it is shown that the effect of coding is similar to increasing X( Omega ) by an additive portion 1/A( Omega ). This favors depressions of A( Omega ) at frequencies where X( Omega ) is poor. However, for A( Omega ) to have any depressions, the signaling rate must be increased with respect to uncoded storage, and this inevitably degrades X( Omega ). At high information densities the degradation is often too large for coding to be rewarding. Examples serve to illustrate these results.>

For a data transmission system with intersymbol interference and noise in which signaling occurs by means of nonoverlapping rectangular pulses, a relation between the equivalent discrete-time models for uncoded and coded transmission is derived. It applies to binary modulation codes with rate R=1/N, where N is a positive integer. Examples suggest that these models are often affected by coding in a manner that is incompatible with a commonly adopted definition of coding gain.>

In digital storage systems, receivers for rate 1/2 modulation codes are usually oversampled by a factor of two with respect to the data stream that they attempt to reconstruct. It is shown that oversampling may be avoided by using partial-response techniques to detect, instead of the encoded binary signal, a decimated ternary one, from which the original data can be recovered by means of a simple decoder. A method is described to find all such decoders for a given rate 1/2 code. Examples treated are FM, MFM, Miller-squared,