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     

A simple fault-diagnosis system with periodic testing

The authors propose a simple diagnostic policy where the system is tested at periodic times nT (n=1, 2, . . .) and undergoes repair after a number N of no-responses. The optimal number N* for minimizing the mean time to some-response is calculated. A numerical example is given     

Periodic-replacement models with threshold levels

The authors suggest five replacement policies where a unit is replaced at periodic times, jT(j=1,2, . . .), and the replacement cost is expensive when some number of events occurring in (0,t) is greater than a threshold level. The usual models for inspection, periodic replacement, block replacement, parallel systems, and cumulative damage can be transformed into replacement models with threshold levels. The mean cost-rate of each model is obtained, using well-known results of reliability theory. The optimum replacement time which minimizes the cost-rate of an inspection model is discussed and shown to exist uniquely     

Signal sets matched to groups

Recently, linear codes over Z_M (the ring of integers mod M) have been presented that are matched to M -ary phase modulation. The general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes. A definition is given for the notion of matching. It is shown that any signal set in N-dimensional Euclidean space that is matched to an abstract group is essentially what D. Slepian (1968) called a group code for the Gaussian channel. If the group is commutative, this further implies that any such signal set is equivalent to coded phase modulation with linear codes over Z_M. Some further results on such signal sets are presented, and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed     

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=∞     

Some results on the norm of codes

Two upper bounds for the norm N(C) of a binary linear code C with minimal weight d and covering radius R are given. The second of these bounds implies that C is normal if R=3     

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     

Nonlinear optical and electrooptical effects in 2-methyl-4-nitro N-methylaniline (MNMA) crystals

Single crystals of 2-methyl-4-nitro-N-methylaniline (MNMA) have been grown from the melt. The crystal structure was determined (orthorhombic, Pna2_I (2 mm), Z=4, a =17.788(6) Å, b=11.893(4) Å, c=3.907(2) Å). The refractive indexes n_a and n_c were measured between 500 and 700 nm [ n_a(633 nm)=2.148(10), n_c(633 nm)=1.520(3)]. The nonlinear optical susceptibilities coefficients r ₃₁=8 pm/V and r₃₃=7.5 pm/V were determined. Most optical properties can be explained in terms of molecular orientation and polarizability     

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     

Calibration of radars using polarimetric techniques

A method that uses the properties of rain medium itself to obtain accurate weather radar system gain calibration is discussed. This technique is based on the principle that the rainfall rate measured using absolute reflectivity (Z) and differential reflectivity ( Z_DR) is the same as that obtained from specific differential phase (K_DP). The measurements required for this technique are Z, Z_DR, and K _DP. The rainfall rate estimates obtained from Z and Z_DR are compared with the estimates obtained from K_DP. The scatter plot between the two rainfall estimates should lie close to a 1:1 line, and any systematic deviation from this line can be removed by appropriately adjusting the system gain. It is noted that Z_DR can be calibrated accurately because it is a differential power measurement, and K_DP is obtained from differential phase measurement, which is unaffected by system calibration. The sensitivity and accuracy of this technique are studied, and theoretical and simulation results for C-band frequencies are presented     

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     

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 note on `Notch Fourier transform' [by Y. Tadokodo and K. Abe]

In the above-titled paper (see ibid., vol.ASSP-35, p.1282, Sept. 1987), Tadokodo and Abe presented a clever method to compute the Fourier coefficients at arbitrary frequencies. But their proof of (16) is incomplete, since in their proof the number of sampled data N is assumed to be power of two (i.e., N=2^q). However, N=2r, where r is the number of frequency components to be analyzed, is not a necessary power of two even in the discrete Fourier transform (DFT) case. The note gives a complete proof on their (16) without any restrictions on N     

Recursive algorithms for calculating the scattering from Nstrips or patches

Using the definition of recursive relations for the reflection operator for N strips or patches, two easily programmable recursive algorithms are developed to calculate the electromagnetic scattering by N strips or patches. One algorithm is for arbitrary excitation, and the other is for a fixed excitation. The recursive algorithms require the inversion of small matrices at each stage and hence are suitable for programming on smaller computers. If the N strips or patches are identical and equally spaced, symmetry can be exploited to speed up the algorithms. A program was developed to calculate scattering by N strips, and the result is shown to converge to scattering by a large strip when the N strips are contiguous     

Potential uses of the differential propagation phase constant toestimate raindrop and hailstone size distributions

One of the Doppler radars operated by the National Severe Storms Laboratory can measure the difference between propagation phase constants K_Dp at horizontal and vertical polarization. This study examines the use of this parameter K _Dp in addition to the reflectivity factor Z_H and the differential reflectivity Z_DR, to obtain information about rain and hail. It is shown from theory and experiments that a third parameter of the drop size distribution, obtained from K_DP, can be used to support Z _DR measurement and/or to point out mixed-phase hydrometeors. Quantitative information on hail size distribution can be obtained for small hailstones when their major axes are nearly vertically aligned, giving rise to negative Z_DR and K_DP values     

A binary analog to the entropy-power inequality

Let {X_n}, {Y_n} be independent stationary binary random sequences with entropy H( X), H(Y), respectively. Let h(ζ)=-ζlogζ-(1-ζ)log(1-ζ), 0⩽ζ⩽1/2, be the binary entropy function and let σ(X)=h^-1 (H(X)), σ(Y)=h^-1 (H(Y)). Let z_n=X_n⊕Y_n , where ⊕ denotes modulo-2 addition. The following analog of the entropy-power inequality provides a lower bound on H(Z ), the entropy of {Z_n}: σ(Z)⩾σ(X)*σ(Y), where σ(Z)=h^-1 (H(Z)), and α*β=α(1-β)+β(1-α). When {Y _n} are independent identically distributed, this reduces to Mrs. Gerber's Lemma from A.D. Wyner and J. Ziv (1973)     

Efficient N×N star couplers using Fourier optics

A technique for constructing an efficient N×N star coupler with large N at optical frequencies is described. The coupler is realized in free space using two arrays, each connected to N single-mode fibers. The highest efficiencies are obtained using a planar arrangement of two linear arrays separated by a dielectric slab serving as free-space region. The coupler is suitable for mass production in integrated form, with efficiencies exceeding 35%     

Systolic arrays for the discrete Hartley transform

Recently, R.N. Bracewell (1983) introduced the discrete Hartley transform (DHT) as an alternative to the discrete Fourier transform (DFT). Two linear systolic array models for the (DHT) are derived. One model requires O(2N-1) in the computational phase and O(N) in the preloading phase. The other model requires O(2N-1) in the computational phase and O(N) in the output phase. A square systolic array for two-dimensional DHT is also constructed by combining the individual advantages of each model. The CORDIC algorithm is proposed as an alternative to conventional multipliers. To speed up the systolic array, two-level pipelining with CORDIC is also possible     

Complete classification of roots to one-dimensional median andrank-order filters

The set of roots to the one-dimensional median filter is completely determined. Let 2N+1 be the filter window width. It has been shown that if a root contains a monotone segment of length N+1, then it must be locally monotone N+2. For roots with no monotone segment of length N+1, it is proved that the set of such roots is finite, and that each such root is periodic. The methods used are constructive, so given N, one can list all possible roots of this type. The results developed for the median filter also apply to rank-order filters     

Perfect N-phase sequences and arrays [spread spectrumcommunication]

Perfect sequences and arrays have periodic autocorrelation functions whose out-of-phase values are zero. Time-discrete N-phase sequences and arrays have complex elements of magnitude one, and one of (2π/N)n, 0⩽n<N , different phase values. Existence conditions and construction methods for perfect N-phase sequences and arrays with a small alphabet of possible phase values are introduced. Combining the existence conditions with, methods of advanced computer search, new perfect N-phase arrays have been found. The resulting lowest number N of perfect N-phase sequences and arrays up to 40 elements are given in a table, after having applied the construction methods