Design of a special family of optical CDMA address codes for fullyasynchronous data communications

A special family of optical address codes, called strict optical orthogonal codes (OOCs), is proposed for fiber-optic code-division multiple access (FO-CDMA) networks. Such codes can strictly guarantee both crosscorrelation and autocorrelation constraints (i.e., λ _c and λ_a) to be one in fully asynchronous data communications and ultrafast switching. Theory of strict OOCs is presented and the code design is described by using the concepts of slot distances. Moreover, the use of strict OOCs can support variable-rate and multirate data communications in an FO-CDMA network with no violation of λ_c=λ_a=1 and no increase of system complexity compared to using conventional OOCs     

Constellations matched to the Rayleigh fading channel

We introduce a new technique for designing signal sets matched to the Rayleigh fading channel, In particular, we look for n-dimensional (n⩾2) lattices whose structure provides nth-order diversity. Our approach is based on a geometric formulation of the design problem which in turn can be solved by using a number-geometric approach. Specifically, a suitable upper bound on the pairwise error probability makes the design problem tantamount to the determination of what is called a critical lattice of the body S={x=(x₁, ···, x_n)∈Rⁿ, |Π_i=1ⁿx_i|⩽1}. The lattices among which we search for an optimal solution are the standard embeddings in R ⁿ of the number ring of some totally real number field of degree n over Q. Simulation results confirm that this approach yields lattices with considerable coding gains     

The dynamics of group codes: state spaces, trellis diagrams, andcanonical encoders

A group code C over a group G is a set of sequences of group elements that itself forms a group under a component-wise group operation. A group code has a well-defined state space Σ_k at each time k. Each code sequence passes through a well-defined state sequence. The set of all state sequences is also a group code, the state code of C. The state code defines an essentially unique minimal realization of C. The trellis diagram of C is defined by the state code of C and by labels associated with each state transition. The set of all label sequences forms a group code, the label code of C, which is isomorphic to the state code of C. If C is complete and strongly controllable, then a minimal encoder in controller canonical (feedbackfree) form may be constructed from certain sets of shortest possible code sequences, called granules. The size of the state space Σ_k is equal to the size of the state space of this canonical encoder, which is given by a decomposition of the input groups of C at each time k. If C is time-invariant and ν-controllable, then |Σ_k|=Π_1⩽j⩽v|F_j/F _j-1|^j, where F₀ ⊆···⊆ Fν is a normal series, the input chain of C. A group code C has a well-defined trellis section corresponding to any finite interval, regardless of whether it is complete. For a linear time-invariant convolutional code over a field G, these results reduce to known results; however, they depend only on elementary group properties, not on the multiplicative structure of G. Moreover, time-invariance is not required. These results hold for arbitrary groups, and apply to block codes, lattices, time-varying convolutional codes, trellis codes, geometrically uniform codes and discrete-time linear systems     

Even-mode characteristics of the bilateral slotline

Transmission line data for the even-mode characteristics of a bilateral slotline (double-sided slotline) are presented. The slotline is analyzed by the spectral Galerkin method, and results are presented for the slot wavelength and characteristic impedance for substrates having ε_r=2.22, 3.5, 6.0, 9.8, and 12.8. The results are presented for 0.01⩽√ε_r-1d/λ ₀⩽0.25, where 2d is the substrate thickness and ε_r its dielectric constant     

Some new constructions for simplex codes

Three constructions for n-dimensional regular simplex codes α_i, 0⩽i⩽n, are proposed, two of which have the property that α_i for 1⩽i⩽n is a cyclic shift of α₁. The first method is shown to work for all the positive integers n=1,2,... using only three real values. It turns out that these values are rational whenever n+1 is a square of some integer. Whenever a (v,k,λ) cyclic (or Abelian) difference set exists, this method is generalized so that a similar method is shown to work with ν=n (the number of dimensions)     

Method for calculating coupling length of Ti:LiNbO3waveguide directional couplers

Reports a theory for calculating the coupling length L _c of Ti:LiNbO₃ single-mode waveguide directional couplers from process parameters and operating wavelength. Estimates are accurate to within a factor of 2 compared with published experimental results for z-cut y-propagating LiNbO₃ devices for 0.63 μm⩽λ⩽1.56 μm. Use of this formalism to assess acceptable process parameter and wavelength tolerances is demonstrated     

On ternary complementary sequences

A pair of real-valued sequences A=(a₁,a₂,...,a_N) and B=(b₁,b ₂,...,b_N) is called complementary if the sum R(·) of their autocorrelation functions R_A(·) and R_B(·) satisfies R(τ)=R_A(τ)+R _B(τ)=Σ_i=1^N$ -^τa_ia_i+τ+Σ_j=1 ^N-τb_jb_j+τ=0, ∀τ≠0. In this paper we introduce a new family of complementary pairs of sequences over the alphabet α₃=+{1,-1,0}. The inclusion of zero in the alphabet, which may correspond to a pause in transmission, leads both to a better understanding of the conventional binary case, where the alphabet is α₂={+1,-1}, and to new nontrivial constructions over the ternary alphabet α₃. For every length N, we derive restrictions on the location of the zero elements and on the form of the member sequences of the pair. We also derive a bound on the minimum number of zeros necessary for the existence of a complementary pair of length N over α₃. The bound is tight, as it is met by some of the proposed constructions, for infinitely many lengths     

Capacity of the Gaussian arbitrarily varying channel

The Gaussian arbitrarily varying channel with input constraint Γ and state constraint Λ admits input sequences x=(x₁,---,X_n) of real numbers with Σx_i²⩽nΓ and state sequences s=(S₁,---,s_n ) of real numbers with Σs_i²⩽nΛ; the output sequence x+s+V, where V=(V₁,---,V_n) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance σ². It is proved that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals 1/2 log (1+Γ/(Λ+σ²)) if Λ<Γ and is 0 otherwise     

Frequency-dependent characteristics of current distributions onmicrostrip lines

The spectral-domain analysis using Chebyshev's polynomials as basis functions is used to obtain the frequency-dependent characteristics of current distributions and the effective relative permittivities of an open microstrip line. The results obtained are compared to other available results. To obtain accurately the current distributions requires a larger number of basis functions. Both longitudinal and transverse current distributions on the strip are shown for wide ranges of frequency (0⩽h/λ₀⩽1)     

Wavelength-tunable electrooptic polarization conversion inbirefringent waveguides

Wavelength-tunable, electrooptic polarization conversion in a birefringent waveguide accomplished with a multiple cascade of alternating TE←→TM mode converter and TE/TM phase shifter sections is analyzed. Such polarization converters have been demonstrated in LiNbO₃ and have been used as electrooptically tunable narrowband (Δλ⩽λ₀/1000) wavelength filters with tuning ranges of at least λ₀/200. It is shown that the polarization converter requires only two independent drive voltages and provides arbitrary polarization transformations from any general input polarization to any desired output polarization with simultaneous wavelength tunability. The device is characterized by its overall transfer matrix and the optical bandwidths and tuning ranges for various electrode geometries     

Effect of grating phase difference on single-mode yield incomplex-coupled DFB lasers with gain and index gratings

In complex-coupled DFB lasers with both index and gain gratings, I have studied the effect of the phase difference between index and gain gratings on the single-mode yield considering the threshold gain difference (side-mode suppression ratio) and the optical field uniformity (spatial hole burning). I have obtained the optimum values of: (1) the phase difference ΔΩ between index and gain gratings, (2) the coupling strength (ℵL)_i of gain grating, and (3) the coupling strength (ℵL)_r of index grating, in order to obtain a high single-mode yield regardless of the relative positions of both facets, The used theory is based on the coupled-mode theory and includes the spatial hole burning correction and the standing wave effect. ΔΩ=π/4 (and 3π/4) DFB lasers with HR-AR facets have the highest single-mode yield and should have ~0.6⩽(ℵL)_i⩽~1.5 and (ℵL)_r<~1.25 in order to obtain above 50% yields. Even above 90% yields can be obtained with the range of ~1.1⩽(ℵL)_i⩽~1.4 and ~0.5⩽(ℵL)_r ⩽~0.85. The superior yield characteristics of ΔΩ=π/4 (and 3π/4) DFB lasers, which is above 2.4 times higher than that of ΔΩ=0 (and π) DFB lasers, comes from their better field intensity uniformity. The results presented in this paper provide insight into the variation of the threshold gain difference and the optical field uniformity with ΔΩ, (ℵL)_r, (ℵL)_i, and (ρ_l, ρ_r)     

The Kolmogorov complexity, universal distribution, and codingtheorem for generalized length functions

A function h(w) is said to be useful for the coding theorem if the coding theorem remains to be true when the lengths |w| of codewords w in it are replaced with h(w). For a codeword w=a₀a₁...a_m-1 of length m and an infinite sequence Q=(q₀, q₁, q₂, ...) of real numbers such that 0n⩽½, let |w|_Q denote the value Σ_n=0^m-1 (if a_n =0 then -log₂q_n, else -log₂(1-q _n)), that is, -log₂, (the probability that flippings of coins generate x) assuming that the (i+1)th coin generates a tail (or 0) with probability q_i. It is known that if 0n→∞ q_n then |w|_Q is useful for the coding theorem and if lim_n→∞ q _n/(1/(2ⁿ))=0 then |w|_Q is not useful. We introduce several variations of the coding theorem and show sufficient conditions for h(w) not to be useful for these variations. The usefulness is also defined for the expressions that define the Kolmogorov complexity and the universal distribution. We consider the relation among the usefulness for the coding theorem, that for the Kolmogorov complexity, and that for the universal distribution     

Gain and saturation intensity of the green Ho:ZBLAN upconversionfiber amplifier and laser

The gain and saturation intensity of the green Ho-doped fluorozirconate (ZBLAN) glass fiber amplifier and laser, pumped in the red (643 ⩽ λ_p ⩽ 649 nm; ⁵F₅ ← ⁵I₈), have been measured. For a 2.4-μm core diameter fiber 45 cm in length, the single-pass gain at 543.4 nm exceeds 12 dB for 90 mW of pump power at 643.5 nm. The saturation power for the ⁵F₄, ⁵S₂ → ⁵I₈ lasing transition was determined from gain measurements to be 970 ± 175 μW, which corresponds to a saturation intensity of 19.8 ± 3.5 kW · cm^-2 , and a stimulated emission cross section approximately one order of magnitude larger than theoretical estimates     

Three messages are not optimal in worst case interactivecommunication

Let X and Y be two jointly distributed random variables. Suppose person P_X, the informant, knows X, and person P_Y, the recipient, knows Y, and both know the joint probability distribution of the pair (X,Y). Using a predetermined protocol, they communicate over a binary error-free channel in order for P_Y to learn X, whereas P_X may or may not learn Y. Cˆm(X|Y) is the minimum number of bits required to be transmitted (by both persons) in the worst case when only m message exchanges are allowed. Cˆ∞(X|Y) is the number of bits required when P_X and P_Y can communicate back and forth an arbitrary number of times. Orlitsky proved that for all (X,Y) pairs, Cˆ₂(X|Y)⩽4Cˆ∞(X|Y)+3, and that for every positive c and ∈ with ∈<1, there exist (X,Y) pairs with Cˆ₂(X|Y)⩾(2-∈)Cˆ₃ (X|Y)⩾(2-∈)Cˆ-∞(X|Y)⩾c. These results show that two messages are almost optimal, but not optimal. A natural question, then, is whether three messages are asymptotically optimal. In this work, the authors prove that for any c and ∈ with 0<∈<1 and c>0, there exist some (X,Y) pairs for which Cˆ₃(X|Y)⩾(2-∈)Cˆ₄(X|Y)⩾c. That is, three messages are not optimal either     

An Algorithm for Universal Lossless Compression With Side Information

This paper proposes a new algorithm based on the Context-Tree Weighting (CTW) method for universal compression of a finite-alphabet sequence x₁ ⁿ with side information y₁ ⁿ available to both the encoder and decoder. We prove that with probability one the compression ratio converges to the conditional entropy rate for jointly stationary ergodic sources. Experimental results with Markov chains and English texts show the effectiveness of the algorithm     

The length of a typical Huffman codeword

If p_i(i=1,···, N) is the probability of the ith letter of a memoryless source, the length l_i of the corresponding binary Huffman codeword can be very different from the value -log p_i. For a typical letter, however, l_i≈-logp_i. More precisely, P_m ^-=Σ/sub j∈{i|l<-logpj-m}/p_j<2^-m and P_m ⁺=Σ/sub j∈{i|li>-logpi+m/}p_j<2^-c(m-2)+2, where c≈2.27     

InGaAlAs-InP quantum-well infrared photodetectors for 8-20-μmwavelengths

We demonstrate the first long-wavelength quantum-well infrared photodetectors using the lattice-matched n-doped InGaAlAs-InP materials system. Samples with AlAs mole fractions of 0.0, 0.1, and 0.15 result in cutoff wavelengths of 8.5, 13.3, and 19.4 μm, respectively, a 45° facet coupled illumination responsivity of R=0.37 μm and detectivity of D_λ*=3×10⁸ cm·√(Hz)· at T=77 K, for a cutoff wavelength λ_c=13.3 μm have been achieved. Based on the measured intersubband photoresponse wavelength, a null conduction band offset is expected for In_0.52Ga_0.21Al_0.27 As-InP heterojunctions     

Binary sequence sets with favorable correlations from differencesets and MDS codes

We propose new families of pseudorandom binary sequences based on Hadamard difference sets and MDS codes. We obtain, for p=4k-1 prime and t an integer with 1⩽t⩽(p-1)/2, a set of p^t binary sequences of period p² whose peak correlation is bounded by 1+2t(p+1). The sequences are balanced, have high linear complexity, and are easily generated