More on the decoder error probability for Reed-Solomon codes

A combinatorial technique similar to the principle of inclusion and exclusion is used to obtain an exact formula for P_E (u), the decoder error probability for Reed-Solomon codes. The P_E(u) for the (255, 223) Reed-Solomon code used by NASA and for the (31, 15) Reed-Solomon code (JTIDS code) are calculated using the exact formula and are observed to approach the Qs of the codes rapidly as u gets large. An upper bound for the expression |P_E(u)/ Q-1| is derived and shown to decrease nearly exponentially as u increases     

Real-time implementation of a narrow-band Kalman filter with afloating-point processor DSP32

The author presents experimental results from two studies. First, a real-time narrowband Kalman filter is implemented with a floating-point digital processor DSP32. The real-time capability of this narrowband filter is investigated by varying parameters Q and R. The covariance matrices Q and R of the dynamic and measurement noise sequences are found to exhibit duality in the real-time tuning process and have a direct effect on system stability. If the value of Q used is smaller (with fixed R ), the tracking time and the narrower tracking bandwidth of the filter will be longer. In addition, if the value of R used (with fixed Q) is smaller, the tracking time will be smaller, and the tracking bandwidth of the filter will be larger. The results are tabulated. Second, two optimal codes (in the sense of the execution speed), straight-line code and general matrix-based code, have been developed for implementing the narrowband Kalman filter. These two codes are compared in terms of program memory size, data memory size, and speed of execution. With the matrix-based code, the DSP32 performance is evaluated in terms of speed and memory size by varying the number of states of a Kalman filter. The results are also tabulated     

Analysis of a type II hybrid ARQ scheme with codecombining

An analysis is presented of the selective-repeat type II hybrid AR Q (automatic-repeat-request) scheme, using convolutional coding and exploiting code combining. With code combining, at successive decoding attempts for a data packet, the decoder for error correction operates on a combination of all received sequences for that packet rather than only on the two most recent received ones as in the conventional type II hybrid ARQ scheme. It is shown by means of analysis and computer simulations that with code combining, a significant throughput is achievable, even at very high channel error rates     

Identities and approximations for the weight distribution of q-ary codes

An explicit formula is derived that enumerates the complete weight distribution of an (n, k, d) linear code using a partially known weight distribution. An approximation formula for the weight distribution of q-ary linear (n, k , d) codes is also derived. It is shown that, for a given q-ary linear (n, k, d) code, the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q=q ^-(n-k) as u becomes large. The error term is a decreasing function of the minimum weight of the dual. The results are also valid for nonlinear (n, M, d) codes with the minimum weight of the dual replaced by the dual distance     

A simple scheme for unity power-factor rectification for highfrequency AC buses

A simple scheme is proposed for offline unity power factor rectification for high-frequency AC buses (20 kHz). A bandpass filter of the series-resonant type, centered at the line frequency, is inserted between the line and the full-wave rectified load. The Q=Z ₀/R_L formed by the load and the characteristic impedance of the tank circuit determines the power factor, the boundary between continuous and discontinuous conduction modes, the peak stresses, and the transient response of the rectifier. It is shown that for Q>2/π the rectifier operates in continuous conduction mode and the output voltage is independent of the load. Also, it is shown that for Q>2 the line current is nearly sinusoidal with less than 5% third-harmonic distortion and the power factor is essentially unity. An increase in Q causes an increase in the peak voltages of the tank circuit and a slower transient response of the rectifier circuit. The DC, small-signal, and transient analyses of the rectifier circuit are carried out, and the results are in good agreement with simulation and experimental results     

Solution and applications of the Lyapunov equation for controlsystems

Recent advances in control systems analysis and design have implied new uses for the Lyapunov equation of the form AX+XA^T+Q=0. Implementation requirements for the incorporation of the use of Lyapunov equations in practical design, however, point out the need for a set of specialized numerical procedures. This special set of numerical procedures must efficiently solve large, sparse Lyapunov equations, solve sets of Lyapunov equations that differ only in the coefficient matrix Q, and provide good low rank estimates of the Lyapunov equation solution X in the case where low rank approximations are applicable. Discussions of the motivations for the solution of these problems and of candidate solution approaches are provided     

Approximate small-signal analysis of the series and the parallelresonant converters

Approximate transfer functions of series and parallel resonant converters are given which are in good agreement with the results of exact analysis as well as the results of experiments. It is shown that the dominant behavior of these transfer functions is determined by the output low-pass filter modified by the internal impedance of the converter. The high-frequency behavior, on the other hand, is given by a second-order response whose frequency is at the difference between the resonant and the switching frequencies and whose Q is the original resonant Q modified by the internal impedance of the converter     

Transient M/M/1 queue variance computation using generalized Q functions

A generalized Q function representation for the transient M/M/1 queue variance is developed. The expression is highly accurate and computationally efficient, and an upper bound on the error is easily calculated. For a Q function relative error of 2×10-¹² using Parl's method, the relative error of the variance is generally less than 10^-9. Average execution time is of the order of 70 ms per point on a VAX 11/750, but faster execution times can be obtained by using larger Q function relative errors     

A VLSI demodulator for digital RF network applications: theory andresults

An all-digital demodulator/detector which is suitable for both analog FM and digital phase/frequency modulations is presented. The system uses complex sampling, which employs a single A/D (analog/digital) converter to sample the signal at an intermediate frequency (IF) and produce baseband in-phase (I) and quadrature phase (Q) signals, and a simplified technique for reducing the effect of the I/Q timing misalignment usually associated with this approach. The system also includes two detectors which operate simultaneously to provide noncoherent and differentially coherent detection, as well as automatic gain control (AGC) and automatic frequency control (AFC). The flexibility afforded by the two concurrent detectors in this all-digital system is shown to make it suitable for a wide range of applications. The theory behind the demodulator/detector system is described, and an implementation using a 1.25-μm bulk CMOS VLSI process is presented. Methods are shown for extending and improving the I/Q sampling misalignment correction technique, as well as for reducing the A/D sampling rate for a given IF frequency. Simulation and experimental results illustrate system performance for both analog and digital modulations     

A self-injection locked, Q-switched, line-narrowed Ti:Al2O3 laser

Line-narrowing, Q-switched, and self-injection locking are studied independently and as a system. Line narrowing is shown both theoretically and experimentally to depend on the inverse square root of the pulse evolution time interval. Q switching of the Ti:Al₂O₃ laser is demonstrated and the laser output energy as a function of the Q-switch delay is investigated. Self-injection is demonstrated and the operation of the laser is explored as a function of loss and the Q-switch delay. Self-injection locking is demonstrated and the performance as a function of the Q-switch delay is determined     

A numerical study of a dielectric disk antenna above groundeddielectric substrate

An antenna made of a dielectric disk with a high permittivity mounted on top of a grounded dielectric substrate of low permittivity is analyzed. A numerical procedure based on surface integral equations, derived from the equivalence principle, is used to compute the natural resonant frequencies for the HEM₁₁ mode from which the radiation Q factor of the antenna is obtained. Then the radiation pattern of the antenna, operating at the resonant frequency evaluated previously, is computed with an electric dipole excitation located within the dielectric substrate under the dielectric disk. The effect of various parameters on the radiation characteristics of the antenna is studied, and presented in the form of diagrams. The low values of the radiation Q, combined with the high values of the dielectric Q and conductor Q, indicate that this antenna promises to be more efficient then the microstrip antenna     

Optimal queueing policies for fast packet switching of mixedtraffic

The power of ATM (asynchronous transfer mode) is its ability to provide bandwidth on demand, different sources can have different bandwidth requirements. Sources also differ in performance requirements, some ask for minimal delay variations, whereas others must have extremely low cell loss probabilities. It is shown how these complementary performance requirements can be explained with an LDOLL (low delay or low loss) queue, where sources get either service priority or storage priority. The space of possible LDOLL queuing policies is very large, even after a justified reduction, the size is still O (2^Q2), Q being the maximum number of ATM cells in the LDOLL queue. Using Markov decision theory and concepts of linear programming, only Q so-called efficient solutions are achieved. These are the LDOLL threshold policies, which are conceptually appealing, robust in performance, and practical from the implementation viewpoint     

Output energy characteristics of optimally pumped rotating mirrorQ-switch lasers

The author develops a simple analytical formula for the key laser resonator and Q-switch parameters of an optimally pumped rotating mirror Q-switch laser. The analytical expression developed relates the maximum attainable single pulse output energy to the laser parameters such as rotating mirror speed, output mirror reflectivity, length of the resonator, and the absorption cross section of the laser media on the basis of the experimentally measured mechanical Q-switch loss form. Good agreement between theory and the output performance of a test Nd-glass laser has been demonstrated     

Optimal codes for minimax criterion on error detection

Nonlinear quadratic codes that are optimal for the minimax error detection are presented. Characteristic functions for these codes are asymptotically bent. For a given block size n and the number of codewords |C|, these codes minimize max Q(e), e≠0, where Q(e) is the conditional error-masking probability, given the error pattern e. The codewords are blocks of n symbols from GF(q). Encoding and decoding procedures for the codes are described     

I/Q channel reversal correcting properties of anSQPSK Costas loop with integrated symbol synchronization

An integrated-carrier loop/symbol synchronizer, using a digital Costas loop with matched arm filters to demodulate staggered quaternary phase-shift keyed (QPSK) signals, is analyzed. An expression is derived for the S curve, parameterized by bit synchronization error. This result suggests that the demodulator structure offers an inherent I/Q channel reversal correcting capability. Computer simulation results are presented that support this conclusion, and suggest that ambiguity resolution performance depends on the ratio of carrier and synchronization loop bandwidths     

Frequency-hopped multiple access communications with coding andside information

The authors consider frequency-hopped spread-spectrum multiple-access communications using M-ary modulation and error-correction coding. The major concerns are multiple-access interference and the network capacity in terms of the number of users that can transmit simultaneously for a given level of codeword error probability. Block coding is studied in detail. The authors first consider the use of Q-ary Reed-Solomon (RS) codes in combination with M-ary modulation with mismatched alphabets so that Q>M. It is shown that the network capacity is drastically reduced in comparison with the system with matched alphabets. As a remedy, the use of matched M-ary BCH codes is proposed as an alternative to mismatched RS codes. It is shown that when the number of users in the system is large, a BCH code outperforms an RS code with a comparable code rate and decoding complexity. The authors consider the use of a robust technique for generation of reliable side information based on a radio-threshold test. They analyze its performance in conjunction with MFSK and error-erasure correction decoding. It is shown that this nonideal ratio-threshold method can increase the network capacity in comparison with the system with perfect side information     

A low-loss bandpass filter using electrically coupled high-Q TM01δ dielectric rod resonators

For a TM_01δ mode dielectric rod resonator placed coaxially in a TM₀₁ cutoff circular waveguide, characteristics such as the resonant frequency, its temperature coefficient, the unloaded Q, and the other resonances are discussed on the bases of accurate calculations using the mode-matching method. The results show that this resonator compares favorably with a conventional TE_01δ mode dielectric resonator, particularly for realization of a high unloaded Q. Analytical results also verify that interresonator coupling between these two resonators can be expressed equivalently by a capacitively coupled LC resonant circuit. A four-stage Chebyshev filter having a ripple of 0.035 dB and an equiripple bandwidth of 27 MHz at a center frequency of 11.958 GHz was fabricated using these resonators. Its insertion loss is 0.5 dB, which corresponds to an unloaded Q of 17000, and no spurious response appears in the frequency range below 17 GHz     

An EMQ-switched CO2 laser as a pump source for afar-infrared laser with a high peak power and a high repetitionrate

A modified current pulsed Q (EMQ)-switched CO₂ laser which is Q-switched by a mechanical beam chopper in combination with a pulsed discharge current is discussed. The laser produces a very stable output with a peak power greater than 1 kW at a repetition rate of 1000 p.p.s. for all transitions in the P and R branches of the CO₂ spectrum. A CH₃F laser pumped by the EMQ-switched laser produces 496 μm radiation in a 6.5 W peak, 100 ns pulses at 500 p.p.s. in the lowest loss EH₁₁ mode     

Lower level relaxation of Nd:YAG

The results of studies on the relaxation rate of the terminal level of the 1.064 μm laser line of Nd:YAG are presented. It is shown that by measuring and modeling the time dependent gain of a Q-switched unidirectional ring oscillator, an upper limit of 11 ns may be placed on the relaxation rate of the ⁴I _11/2 level     

Control of batch processing systems in semiconductor waferfabrication facilities

Loading policies for a batch processing machine, i.e. a machine that can process more than one job at a time, when the arrival times of jobs to the machine are uncertain, are described. The motivation for the study is the structure of process flows and the predominance of batch processing systems in a semiconductor wafer fabrication facility. A two stage serial-batch system with the serial stage (e.g. photolithography) feeding the batch (e.g. furnace) is considered. Machines in the serial stage process one job at a time; further, these machines are subject to failure. A control limit policy for loading the batch machine is assumed, i.e. load if the queue length ⩾Q, else wait until the number of jobs in queue is at least Q. The basic tradeoffs considered are delay (waiting too long) vs. capacity utilization (loading early with very few jobs). An average cost analysis is done and optimized to compute the critical number Q. In an extension to the basic model, the effect of due dates on the critical number is analyzed. Comparison with simulation results is very encouraging