Decision depths of convolutional codes

The decision depth function of a convolutional code L_D(w) is the first trellis depth at which all unmerged incorrect subset paths exceed weight w. The authors tabulate this function for most codes in common use. L _D(w) specifies the path memory length of a decoder. It follows a clear asymptotic growth rule     

On the VLSI implementation of real-time order statistic filters

Real-time implementation of an order-statistic filter (OSF) or ranked order filter requires the computation of the order statistic (ranked order) of the samples in a window which gets periodically updated with the arrival of a new sample(s). The authors give an algorithm for the computation of the running order statistic. A highly parallel architecture suitable for VLSI implementation is presented. The architecture is very versatile, with programmable window size and rank order. An expansion algorithm and its VLSI architecture, which permit the usage of two r-bit OSFs to implement an (r+1)-bit OSF, where r is the resolution of the input signal samples, are given. In a special case where one is satisfied with at most one LSB error, the hardware complexity of the proposed architecture can be reduced by almost one half. It is further shown how a VLSI chip incorporating the proposed architecture can be used as the basic building block in the real-time implementation of other forms of nonlinear filters     

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=∞     

4-phase sequences with near-optimum correlation properties

Two families of four-phase sequences are constructed using irreducible polynomials over Z₄. Family A has period L =2^r-1. size L+2. and maximum nontrivial correlation magnitude C_max⩽1+√(L+1), where r is a positive integer. Family B has period L=2(2^r-1). size (L+2)/4. and C_max for complex-valued sequences. Of particular interest, family A has the same size and period as the family of binary Gold sequences. but its maximum nontrivial correlation is smaller by a factor of √2. Since the Gold family for r odd is optimal with respect to the Welch bound restricted to binary sequences, family A is thus superior to the best possible binary design of the same family size. Unlike the Gold design, families A and B are asymptotically optimal whether r is odd or even. Both families are suitable for achieving code-division multiple-access and are easily, implemented using shift registers. The exact distribution of correlation values is given for both families     

A nonsorting VLSI structure for implementing the (M, L) algorithm

A nonsorting structure for implementing the (M, L) algorithm is presented. The processing is based on a survivor selection operation that incorporates parallelism and has an execution time proportional to the product of the logarithm of bM (the number of contender paths), and k (the number of bits used for path metrics). Aside from the path extender(s), the processor area is only a small fraction of the total chip area; most is simply for required storage of path histories and metrics. This means that the structure can support a large M on a single chip. In addition, the structure can be extended to larger M by stacking rows of a few different types of custom chips     

A strengthening of the Assmus-Mattson theorem

Let w₁=d,w₂,…,w _s be the weights of the nonzero codewords in a binary linear [n,k,d] code C, and let w' ₁, w'₂, …, w'₃, be the nonzero weights in the dual code C1. Let t be an integer in the range 0<t<d such that there are at most d-t weights w'_i with 0<w'_i ⩽n-t E. F. Assmus and H. F. Mattson, Jr. (1969) proved that the words of any weight w_i in C form a t-design. The authors show that if w₂⩾d+4 then either the words of any nonzero weight w_i form a (t+1)-design or else the codewords of minimal weight d form a {1,2,…,t,t+2}-design. If in addition C is self-dual with all weights divisible by 4 then the codewords of any given weight w_i form either a (t +1)-design or a {1,2,…,t,t+2}-design. The proof avoids the use of modular forms     

An efficient algorithm for determining the dispersioncharacteristics of single-mode optical fibers

An efficient algorithm is proposed for calculating the dispersion characteristics of optical fibers with radially arbitrary refractive-index profiles. It is based on a variational finite-element formulation. Formulas for the derivatives of the normalized propagation constant w with respect to the normalized frequency V up to the second order are derived by using a reaction formula. These formulas contain the modal field ψ and its derivative dψ/dV. Two variational problems are then formed and solved as matrix equations by using the finite-element method. The first one is a conventional eigenvalue problem with eigen-solution {w,ψ} and dominates the computing time. The second one is a direct problem for dψ/dV and can be solved by a few simple matrix manipulations. The proposed algorithm turns out to be a rapidly convergent one and careful arrangement results in saving for both storing memory and computing time     

Optimality property of the Gaussian window spectrogram

It is shown that for any signal x(t) the minimum of ∫_-∞^∞∫_-∞ ^∞ [(t-t_x)²+(f-f _x)²] S_x^(w)(t , f) dt df over all normalized time-windows w(t) is achieved by the Gaussian window w(t)=2^1/4 exp (-πt²). Here (t_x, f _x) is the center of gravity of the signal x(t ), S_x^(w) (t, f) is the spectrogram of x(t) due to the window w( t), and the double integral is a measure of the spread of S _x^(w) (t, f) around (t _x, f_X) in the time-frequency plane     

In the optimum design of the block adaptive FIR digital filter

A general optimum block adaptive (GOBA) algorithm for adaptive FIR (finite impulse response) filtering is presented. In this algorithm, the correction terms for the filter coefficients in each block, instead of the convergence factors, are optimized in a least squares sense. There are no constraints on the block length L and the filter tap number N. It is shown that the GOBA algorithm is reduced to the normalized LMS algorithm when L⩾N. The convergence of the GOBA algorithm can be assured if the correlation matrix of the input signal is positive definite. Computer simulations based on an efficient computing procedure confirm that the GOBA algorithm achieves faster convergence with slightly degraded convergence accuracy in stationary environments and better weight tracking capability in nonstationary environments as compared to existing block adaptive algorithms with no constraints on L and N     

On the three-coefficient window family

The definition of the three-coefficient window family is extended to the form: w(t,b)=0.5(1-b)+0.5 cos(2πt/T)+0.5b cos(4πt/T ), |t|⩽T/2, -0.25⩽b⩽0.25, and its spectral behavior is investigated. It is found that with the parameter b adjusted to different values, this window family can attain a minimum main lobe width of 1.38, a maximum sidelobe attenuation of 64.19 dB, and a highest cutoff rate of 30 dB/oct     

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     

Cladding layer thickness-controlled directional coupler opticalswitch

The AlGaAs/GaAs cladding layer thickness-controlled directional coupler optical switch (CTC-SW) is discussed. To increase the efficiency of coupling between two waveguides, the CTC-SW was designed with a thin i-AlGaAs cladding layer h between the two waveguides. The coupling length L_c can be reduced, without reduction of the extinction ratio and increase of the switching voltage. For instance, L_c of CTC-SW (h=0.07) can be reduced 40% more than that of a conventional directional coupler switch (h=0). The extinction ratio is near 20 dB, both for the crossover (applied voltage V=0 V) and straight-through (V =19 V) states. A technique for adjusting L_c to the device length was developed     

Error-correcting codes for list decoding

In the list-of-L decoding of a block code the receiver of a noisy sequence lists L possible transmitted messages, and is in error only if the correct message is not on the list. Consideration is given to (n,e,L) codes, which correct all sets of e or fewer errors in a block of n bits under list-of-L decoding. New geometric relations between the number of errors corrected under list-of-1 decoding and the (larger) number corrected under list-of-L decoding of the same code lead to new lower bounds on the maximum rate of (n,e,L) codes. They show that a jammer who can change a fixed fraction p<1/2 of the bits in an n-bit linear block code cannot prevent reliable communication at a positive rate using list-of- L decoding for sufficiently large n and an L⩽n. The new bounds are stronger for small n , but weaker for fixed e/n in the limit of large n and L than known random coding bounds     

Vector sets for exhaustive testing of logic circuits

(L, d)-universal sets are useful for exhaustively testing logic circuits with a large number of functional components, designed so that every functional component depends on at most d inputs. Randomized and deterministic constructions of ( L, d)-universal test sets are presented, and lower and upper bounds on the optimal sizes of such sets are proven. It is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an NP-complete problem     

Effect of parameter variations on the performance of GaAs/AlGaAsmultiple-quantum-well electroabsorption modulators

A theoretical investigation is presented of the dependence of electroabsorption in GaAs/Al_xGa_1-xAs multiple-quantum-well (MQW) structures on the MQW parameters (Al mole fraction x, well thickness L_z barrier thickness L_b and interface quality) and on the applied electric field studied. The on/off ratio of a modulator using MQWs with x=0.45, L_z=75 Å, and L _b=78 Å is predicted to increase by 20% compared to that of a modulator using MQWs with x=0.3, L_z =100 Å, and L_b=100 Å, when the MQW total active region thickness is 1 μm     

Balancing sets of vectors

For n>0, d⩾0, n≡d (mod 2), let K(n, d) denote the minimal cardinality of a family V of ±1 vectors of dimension n, such that for any ±1 vector w of dimension n there is a v∈V such that |v- w|⩽d, where v-w is the usual scalar product of v and w. A generalization of a simple construction due to D.E. Knuth (1986) shows that K(n , d)⩽[n/(d+1)]. A linear algebra proof is given here that this construction is optimal, so that K(n, d)-[n/(d+1)] for all n≡d (mod 2). This construction and its extensions have applications to communication theory, especially to the construction of signal sets for optical data links     

Light-to-input nonlinearities in an R-LED series network

The light-to-current (L-I) and light-to-voltage (L-V) differential nonlinearities in the simple network of a customary LED and an external resistor R in series are analyzed and calculated theoretically and compared with experimental data. Particular emphasis is placed on the influence of the log-arithmetic slope ν of the L-I characteristic and the bias current I upon the ratio of the corresponding nonlinearity parameters. It is thus deduced that, for a given optical power P, over superlinear portions of the L-I curve (ν>1) the L-I linearity is typically better than its corresponding L-V linearity. On the contrary, when the L-I dependence is sublinear (ν<1) the voltage driving scheme may ensure for the R-LED network, or the LED alone, a local L-V response much more linear than the L-I response, provided that appropriate (optimum) I and/or R values are chosen     

The transfer function and impulse response of photorefractivetwo-beam coupling

The transfer function and impulse response of photorefractive two-beam coupling are derived in the undepleted pump approximation. For sufficiently strong coupling ΓL, the impulse response features a broad delayed output pulse. In the limits of negligible and strong absorption αL, this coupling threshold reads ΓL_thr=4 and Γ_thr=2α, respectively. The time delay and pulse height are functions of the coupling ΓL, the photorefractive time constant τ, and the effective absorption αL. Experiments on a BaTiO₃ crystal measuring the absoluted square of its transfer function and the impulse response are used to determine the coupling and time constant     

A limit theorem for n-phase Barker sequences

It is proved that for 3⩽L⩽19, except for L =6, the total number of normalized n-phase Barker sequences of length L increases without limit as n goes to infinity