New optimum binary shortened cyclic codes with redundancy r = 32 and burst-error correction capability b are presented. The codes are found by performing an exhaustive computer search using the Kasami algorithm, and their performance is compared with analytical bounds by Reiger, Abramson and Campopiano. The true burst-error correction capability of the [2112, 2080] shortened Fire code selected for 10 Gb/s Ethernet is determined to be b = 11 and [2112, 2080] shortened cyclic codes with higher burst-error correction capability b = 13 are given. The double burst-error detection properties of three cyclic redundancy check codes used in standards are compared.

We consider high-rate modulation codes satisfying tight global and interleave (G, I) constraints for magnetic storage systems. We use a novel sliding-window substitution coding technique to improve on known long capacity-efficient (G = 2γ, I = γ) codes. This coding technique maps one-sided (G = 2γ, I = γ)-constrained sequences into one-sided sequences satisfying a substantially tighter G constraint and a slightly relaxed I constraint. Sliding-window substitution encoding in conjunction with enumerative encoding provides high-rate capacity-efficient codes that are relevant for practical magnetic storage systems.

Frame synchronization is studied for pulse-position modulation-encoded longitudinal position (LPOS) words that are embedded in servo patterns written on tape. After introducing soft-output detection of LPOS symbols, the problem of LPOS frame synchronization using soft outputs from the LPOS detector is considered. An efficient LPOS frame-synchronization algorithm that is robust in the presence of transition noise found in magnetic recording channels is then proposed. Finally, the performance of hard-decision LPOS frame synchronization is compared by simulations with that of the proposed soft-decision algorithm, and a hardware implementation of the overall scheme is illustrated.

A reverse concatenation scheme based on an efficient modulation encoder satisfying non-uniform constraints, a systematic Reed-Solomon encoder and a partial symbol interleaver is presented. This architecture achieves very tight modulation constraints and minimizes error propagation and rate loss. The modulation constraints considered are of the same type as the constraints that have been used in generalized partial-response maximum-likelihood (PRML) detection systems. A class of codes that is based on serial concatenation of a prefix-constrained code and two interleaved enumerative codes with non-uniform constraints is proposed. Specific rate-199/200 PRML(G, I) codes are constructed.

Efficient combination of a modulation code with a parity-check code is studied for magnetic recording systems. A new approach to the design of combined modulation/parity codes that largely retains the properties of the original modulation code is proposed. It is based on the matrix transformation of a set of desired parity-check equations at the partial-response channel input into a set of parity-check equations at the input of the precoder. The code design methodology is illustrated by constructing a rate-96/104 dual-parity code that satisfies maximum transition run constraints. Simulation results for a Lorentzian recording channel show that this code significantly outperforms a single-parity code for channels dominated by electronics noise. Moreover, the rate-96/104 dual-parity code, which has been used extensively in commercial disk drives, performs as well as a single-parity code in stationary/nonstationary data-dependent noise conditions. Finally, the low-average-transition-density constraint is proposed to enhance error-rate performance in channels dominated by transition noise.

To mitigate transition noise in magnetic recording is to reduce the number of transitions that are written onto the media. This leads one to consider an average transition density (ATD) constraint. This new constraint reduces the ATD of sequences at the channel input and can be imposed in addition to other constraints. In this paper ATD constraint is imposed which is based on assigning a particular cost function to a finite-state transition diagram (FSTD) that presents a constrained system of binary NRZI sequences. At a normalized linear user density the performance of an unconstrained system satisfying an ATD constraint was simulated using a microtrack longitudinal (Lorentzian) recording model corrupted by transition noise and electronics noise.

Approximations to the union bound performance of sequence detection in the presence of colored noise and an algorithm to compute bit error and error event probabilities are presented and compared to bit-by-bit simulation results. These computations, which are very accurate at bit error probabilities /spl les/10/sup -3/, are then used to analyze the performance of standard and reverse concatenated Reed-Solomon(RS)/modulation coding schemes for generalized partial-response channels corrupted by colored noise. The analysis is used to determine the optimum RS code rate for recording systems that are of current interest.

A new twins constraint for maximum transition run (MTR) codes is introduced to eliminate quasi-catastrophic error propagation in sequence detectors for generalized partial response channels with spectral nulls both at dc and at the Nyquist frequency. Two variants of the twins constraint that depend on whether the generalized partial response detector trellis is unconstrained or j-constrained are studied. Deterministic finite-state transition diagrams that present the twins constraint are specified, and the capacity of the new class of MTR constraints is computed. The connection between (G,I) constraints and MTR(j) constraints is clarified. Code design methodologies that are based on look-ahead coding in combination with violation detection/substitution as well as on state splitting are used to obtain several specific constructions of high-rate MTR codes.

A robust error control scheme for data transmission in CDMA-based cellular systems is proposed which employs outer Reed-Solomon codes concatenated with inner convolutional codes. The performance of this scheme is analyzed assuming nonperiodic random spreading sequences and a Rake receiver with perfect knowledge of the channel. In particular, a simple model for the memoryless inner coding channel that encompasses the effects of multiple access interference, self-noise and thermal noise is first derived. Using new tight upper bounds on bit- and symbol-error probabilities of convolutional codes over Nakagami, Rayleigh, and Rician fading multipath channels, the performance of the concatenated coding scheme is then evaluated. The Reed-Solomon/convolutional coding scheme has been adopted by the European RACE Project Code Division Testbed (CODIT) and implemented in an experimental testbed. The code design methodology, which has been used to specify the 9.6-, 64-, and 128-kbit/s data traffic channels of the CODIT testbed, is presented and the single-cell CDMA capacity is computed.

The problem of preventing quasi-catastrophic error propagation in maximum-likelihood and reduced-state sequence detection for multilevel partial-response channels with transfer functions (1-D/sup P/) and (1+D/sup P/) is studied. M-ary channel input sequences that limit the length of minimum distance error events to L symbols are exhaustively characterized by finite-state transition diagrams. An efficient procedure for computing the capacity associated with these transition diagrams is given. Efficient constrained codes that can be readily implemented by finite-state encoders and block decoders with small error propagation are constructed.>

An error control scheme for data transmission in code division multiple access (CDMA) cellular systems is proposed. The forward error correction scheme employs Reed-Solomon (RS) outer codes concatenated with convolutional inner codes. New tight upper bounds on the convolutional code performance in independent Rayleigh fading multipath channels are derived. Using these bounds and invoking the Gaussian assumption for the multiple access interference, the performance of the concatenated coding scheme is evaluated. Furthermore, design examples of RS outer codes and convolutional inner codes for data transmission at 9.6 and 128 kbit/s in CDMA cellular systems are presented. Finally, the capacity of a CDMA cellular system employing the proposed concatenated coding scheme is computed.>

The realization of a digital recording system using partial-response class-IV signaling with maximum-likelihood sequence detection (MLSD) is described. To perform MLSD at the high data rates encountered in recording systems, a simple implementation of the Viterbi detector based on a difference-metric algorithm is developed. Decision-directed schemes for gain control and timing recovery, for tracking variations of the gain and timing phase during data readback, and for fast initial adjustment from a known preamble are presented. The dynamic behavior of the control algorithms was studied by computer simulations. Coding was used to facilitate timing recovery and gain control, to limit the path memory length of the Viterbi detector, and to allow fast and reliable startup of the receiver. The design and properties of rate 8/9 constrained codes are examined. The problem of equalization is addressed, and analog and combined analog/digital filter implementations are developed. A simple adaptive equalizer capable of compensating variations of the recording channel characteristics with track radius and/or head-to-medium distance is described.>

Multi level sequences with a spectral null of order M at frequency f, meaning that the power spectral density, and its first 2M-1 derivatives vanish at f, are characterized by finite-state transition diagrams (FSTDs) whose edge labels satisfy bounds on the variation of the Mth-order running digital sum (RDS). Necessary and sufficient conditions for FSTDs with higher order null constraints at DC and at an arbitrary submultiple of the symbol frequency are derived. Analytical results are given concerning the performance of codes satisfying an Mth-order RDS constraint on partial-response channels. Specific code designs for quaternary channel inputs are presented. The Euclidean distance properties of this new class of codes, aside from their spectral-shaping properties, are demonstrated.>

Results are presented concerning the noise-free false lock problem in quadriphase receivers with unequal I-channel and Q-channel data rates. It is shown that false lock may occur when the incoming carrier frequency and the loop VCO (voltage-controlled oscillator) frequency differ by an amount that is a linear combination of a quarter of I-channel and Q-channel data rates. General expressions for the false lock performance of quadriphase receivers are given for random as well as periodic data patterns. Specific closed-form expressions for the false lock margin are derived when the arm filters of the quadriphase receivers are single-pole Butterworth filters, and the format of the random data is NRZ (nonreturn-to-zero). Numerical evaluations of false lock margin as a function of the product of 3 dB arm-filter bandwidth and symbol duration are carried out for random data using various arm filters and for different periodic I-channel and Q-channel data patterns.>

Two types of master-slave networks are investigated: oneway and two-way master-slave networks. The one-way master-slave System is a generalization of the well-known hierarchical master-slave tree system. The two-way master-slave system is a novel concept. Sufficient stability conditions are given for both network types. After synchronization is achieved, the frequency drift rate of all oscillators in the network approaches the frequency drift rate of the master oscillator. The steady-state frequency differences between the oscillators and their variances are computed for six network configurations of practical interest. A performance comparison for different network connectivities shows that the two-way master-slave system with a star configuration has the best performance.