A linear lightwave Benes network

The authors consider linear lightwave networks with a single waveband that have N inputs, each with a transmitter, and N outputs, each with a receiver, interconnected by optical links, broadcast stars, and wavelength-independent 2×2 switches. The transmitters and receivers can tune to C different wavelengths. The authors describe a rearrangeably nonblocking network that is a modification of the Benes network and uses transmitters that are fixed tuned and switches with two states. The network uses [1+o(1)] N/log₂(N/C) switches, which is shown to be nearly the minimum number. It is also shown that, if C =o(log N), then a rearrangeably nonblocking network requires [1+o(1)]Nlog₂N switches even if the switches have more than two states     

Error performance of a digitally processed binary ESK frequencyhopping receiver in the presence of large Doppler

Analysis is made of the effects of Doppler on the error rate performance of a low data rate binary FSK frequency hopping receiver, employing a discrete Fourier transform (DFT) technique for baseband detection. Bit detection decision is made by locating the maximum of the DFT outputs which, in the frequency domain, are assumed to be separated by 1/T where T is the bit period. Both the worst case and average error performances are obtained and presented as a function of E_b/N₀ for various values of M where E_b/N₀ is the signal bit energy-to-noise density ratio and M is the degree of freedom associated with the Doppler uncertainty window. The E _b/N₀ degradation as a function of M is also presented     

Noise caused by semiconductor lasers in high-speed fiber-opticlinks

Theoretical and experimental results are presented for the signal-to-noise (S/N) ratio caused by mode partition noise, intensity noise, and reflection-induced noise in optical data links. Under given conditions an additional noise source with a S /N ratio of 20 dB will cause a power penalty of 1 dB in order to maintain a 10^-9 bit error rate. From numerical simulations the authors predict the maximum allowable dispersion in the presence of mode partition noise to be approximately 40% of a clock period. This figure is almost independent of bit rate and laser structure and agrees well with the measurements and with results of other workers. Numerical simulations of a buried-heterostructure and a TJS laser were carried out at four bit rates from 565 Mbit/s to 4.5 Gbit/s and the measurements were done at 2.2 Gbit/s using a TJS laser     

Digital frequency estimation in burst mode QPSK transmission

In burst digital transmission using PSK (phase shift keying) modulation with coherent detection, the recovery of the carrier reference phase and the symbol clock is a key aspect. If all users have a common clock synchronization, symbol timing needs not to be recovered in each burst. A digital processor for carrier recovery without preambles, in the presence of frequency offset, is considered. As an example, a 2 Mb/s QPSK transmission system is considered in which E _b/N_o=10 dB, and the burst and estimation interval length L=15. Using the algorithm described and averaging eight successive estimated frequency offsets, in order to eliminate anomalous errors, the BER (bit error rate) degradation is equal to 0.14 dB when Δf=20 kHz     

Multistate self-electrooptic effect devices

Multistate self-electrooptic-effect devices (M-SEEDs) containing several quantum-well diodes in series are discussed. It is shown that a device with N diodes in series with a voltage source and illuminated by N diodes in series with a voltage source and illuminated by N light beams has N stable states corresponding to any one (and only one) of the diodes being highly transmissive. This voltage-biased M-SEED can perform contention resolution in the sense required by analog systems, because the diode illuminated by the weakest beam becomes the highly transmitting one on powering up the system. A current-biased M-SEED with N diodes in series with a current supply can have 2^N stable states, corresponding to any combination of diodes in their transmitting or absorbing states. This same device can also function as a binary image thresholder. The M-SEEDs are multistable in multiple beams, in contrast to previous multistable optical devices that have multiple states for one beam. Electrically and optically enabled symmetric SEEDs (S-SEEDs) that comprise a pair of quantum-well p-i-n diodes in series with a transistor or a third diode are also discussed. This device is the equivalent of an electrical tristate device that is used in some bus architectures     

Secret key agreement by public discussion from common information

The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y, respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution P_XYZ, can also receive all messages exchanged by the two parties over a public channel. The goal of a protocol is that the enemy obtains at most a negligible amount of information about S. Upper bounds on H(S) as a function of P_XYZ are presented. Lower bounds on the rate H (S)/N (as N→∞) are derived for the case in which X=[X₁, . . ., X _N], Y=[Y₁, . . ., Y_N] and Z=[Z₁, . . ., Z_N] result from N independent executions of a random experiment generating X_i, Y_i and Z_i for i=1, . . ., N. It is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels, even when the enemy's channel is superior to the other two channels     

On the Hamming distance properties of group codes

Under certain mild conditions, the minimum Hamming distance D of an (N, K, D) group code C over a non-abelian group G is bounded by D⩽N -2K+2 if K⩽N/2, and is equal to 1 if K>N/2. Consequently, there exists no (N, K, N-K+1) group code C over an non-abelian group G if 1<K<N. Moreover, any normal code C with a non-abelian output space has minimum Hamming distance equal to D=1. These results follow from the fact that non-abelian groups have nontrivial commutator subgroups. Finally, if C is an (N, K, D) group code over an abelian group G that is not elementary abelian, then there exists an (N, K, D) group code over a smaller elementary abelian group G'. Thus, a group code over a general group G cannot have better parameters than a conventional linear code over a field of the same size as G     

Asymptotically optimal classification for multiple tests withempirically observed statistics

The decision problem of testing M hypotheses when the source is Kth-order Markov and there are M (or fewer) training sequences of length N and a single test sequence of length n is considered. K, M, n, N are all given. It is shown what the requirements are on M , n, N to achieve vanishing (exponential) error probabilities and how to determine or bound the exponent. A likelihood ratio test that is allowed to produce a no-match decision is shown to provide asymptotically optimal error probabilities and minimum no-match decisions. As an important serial case, the binary hypotheses problem without rejection is discussed. It is shown that, for this configuration, only one training sequence is needed to achieve an asymptotically optimal test     

Syndrome and transition count are uncorrelated [logic circuittesting]

In the testing of logic circuits, two proposed data-compression methods use the number of ones (syndrome) and the number of sequence changes (transition count). An enumeration N(m, k , t) of the number of length-m binary sequences having syndrome value k and transition count t is developed. Examination of this result reveals that the parallel compression of these two methods has small overlap in error masking. An asymptotic expression for N(m, k, t) is developed     

Phase-locked laser array far-field normalization

The normalization of the far-field distribution from phase-locked linear arrays of evanescently coupled semiconductor diode lasers is evaluated. As the element number N→∞, the peak irradiance of the fundamental array mode tends to 81% of the peak irradiance of an array of in-phase equal-intensity diodes. It is also found that for N⩾10, the peak irradiance is proportional to 0.81 (1+1/N)N², and the diffraction-limited beamwidth is approximately 1.19 λ(N+1)S where λ is the vacuum wavelength and S is the array period. The far-field array factor is the same for an N-element array and an (N+1) S-wide cosine source as long as N⩾10     

Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_m for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E_b/N₀) and E_b is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

Nonblocking property of reverse banyan networks

The authors present a new nonblocking property of the reverse banyan network under a particular input packet pattern at the input ports. The reverse banyan network is the mirror image of the banyan network. If the input packets of the N×N reverse banyan network have consecutive output address as modulo N, then the reverse banyan network is nonblocking. The routing of packets in the reverse banyan network is described, and the nonblocking property of the reverse banyan network is proved. A possible application of this property in the switching network is discussed     

Optimal life testing schedule for multiple types of integratedcircuits

Life testing of highly reliable integrated circuits (ICs) is a time-consuming process because it usually takes a long time before an IC fails. Several methods have been proposed in the literature to reduce the time required for testing one type of IC. The author considers the problem of estimating the mean life of I types of IC (I>1). Assuming that the lifetime distribution of the ICs is exponential and at most N ICs can be tested concurrently, it is shown that the optimal life testing schedule that requires the smallest mean testing time is to test N ICs of type 1, then test N ICs of type 2,. . . and finally test N ICs of type I      

Performance analysis of nonblocking packet switch with input andoutput buffers

The performance of nonblocking packet switches such as the knockout switch and Batcher banyan switch for high-speed communication networks can be improved as the switching capacity L per output increases; the switching capacity per output refers to the maximum number of packets transferred to an output during a slot. The N×N switch with L=N was shown to attain the best possible performance by M.J. Karol et al. (1987). Here a N×N nonblocking packet switch with input and output buffers is analyzed for an arbitrary number of L such that 1⩽L⩽N. The maximum throughput and packet loss probability at input are obtained when N=∞     

Quadtree-structured recursive plane decomposition coding of images

The approximation of two-dimensional highly correlated grey value functions can be performed using a linear model of the type f( x, y)=a+bx+cy. The set of plane parameters (PPs) [a, b, c] can be determined in the least squares sense for a block of size N×N pixels, for example. Starting with a block size of 2×2 pixels, it is shown that the PPs obey a recursive law such that the PPs of a 2N×2N block can be computed recursively when only the PPs of the four adjacent subblocks of size N×N in the lower decomposition level are known. This concept of recursive plane decomposition (RPD) is embedded in a quadtree data structure to obtain a new variable block size image coding algorithm that offers a high performance at a low computational cost. Extensive comparisons to other state-of-the-art image coding algorithms are reported     

The generalized eigenproblem: pole-zero computation

A modification-decomposition (MD) method is used to compute linear system transfer function poles and zeros by transforming an N-dimensional generalized eigenvalue problem to an M-dimensional standard eigenvalue problem with M⩾ r, where r is the lesser of the ranks of the dynamic or nondynamic component matrix of the system. Hence, network eigenvalue problems normally solved by applying the QZ algorithm directly, or after deflation preprocessing, are solvable with the more efficient QR algorithm. It is shown that the flop (floating-point operations) count for MD-QR algorithms is always less than the flop count for the most efficient deflation-QZ algorithms. For r⩽N, the MD-QR algorithms are exceptionally efficient. Using a parameter matrix decomposition of the dynamic or nondynamic component matrix, the MD method gives physical insight, and it provides a general proof of manifold constraints relating network time constants and poles and zeros. From these relations, accurate dominant and subdominant pole approximations are derived. A general eigenvalue sensitivity formula and a very flexible method for computing eigenvectors is developed and applied to pole sensitivity computation     

Upper bounds on the probability of sequences emitted byfinite-state sources and on the redundancy of the Lempel-Ziv algorithm

An upper bound on the probability of a sequence drawn from a finite-state source is derived. The bound is given in terms of the number of phrases obtained by parsing the sequence according to the Lempel-Ziv (L-Z) incremental parsing rule, and is universal in the sense that it does not depend on the statistical parameters that characterize the source. This bound is used to derive an upper bound on the redundance of the L-Z universal data compression algorithm applied to finite-state sources, that depends on the length N of the sequence, on the number K of states of the source, and, eventually, on the source entropy. A variation of the L-Z algorithm is presented, and an upper bound on its redundancy is derived for finite-state sources. A method to derive tighter implicit upper bounds on the redundancy of both algorithms is also given, and it is shown that for the proposed variation this bound is smaller than for the original L-Z algorithm, or every value of N and K     

Fast computation of transform coefficients for a subadjacent blockfor a transform family

The authors examine several different kinds of subadjacent blocks, and consider fast computation for a transform family including the Walsh-Hadamard transform and the Rh transform as special cases. The approach proposed here provides a direct frequency-frequency procedure. Results indicate that, for this transform family, a reduction of the number of multiplications and additions is achieved by a factor of two-thirds. An example for the Rh transform shows that further reduction of arithmetic operations is also possible. The results of this method are even better for the Walsh-Hadamard transform. The new algorithms can reduce the number of additions from the level O(N log ₂ N) to the level O(N), as compared to the traditional method     

Fast cosine transform of Toeplitz matrices, algorithm andapplications

A fast algorithm for the discrete cosine transform (DCT) of a Toeplitz matrix of order N is derived. Only O(N log N)+O(M) time is needed for the computation of M elements. The storage requirement is O(N). The method carries over to other transforms (DFT, DST) and to Hankel or circulant matrices. Some applications of the algorithm are discussed     

A WDM cross-connected star topology for multihop lightwave networks

The authors propose a star topology for multihop lightwave networks in which the conventional N×N passive star coupler is replaced by fixed wavelength division multiplexed (WDM) cross connects. The proposed topology overcomes three major limitations of the conventional star topology. First, it reduces the number of wavelengths needed in a (p,k) ShuffleNet from kp ^k+1 wavelengths in the conventional topology to p wavelengths in the proposed one. Second, the signal power loss due to the 1/N power splitting at the star coupler no longer exists in the WDM cross connects and, therefore, the restriction on the supported number of users by the star network is alleviated. Third, it completely eliminates the need for wavelength filtering at the input to the receivers as is the case in the conventional star topology