Optical orthogonal codes-new bounds and an optimal construction

A technique for constructing optimal OOCs (optical orthogonal codes) is presented. It provides the only known family of optimal (with respect to family size) OOCs having λ=2. The parameters (n ,ω,λ) are respectively (p^2m-1, p^m+1,2), where p is any prime and the family size is p^m-2. Three distinct upper bounds on the size of an OOC are presented that, for many values of the parameter set (n,ω,λ), improve upon the tightest previously known bound     

Evidence for continuous visible chemical lasing from the fast nearresonant energy transfer pumping of atomic sodium

Energy transfer from selectively formed metastable states of SiO is used to pump sodium-atom laser amplifiers at λ≈569 nm (4d²D-3p²P), λ≈616 nm (5s²S-3p² P), and λ≈819 nm (3d²D -3p²P). The a³Σ⁺ and b³Π states of SiO are generated in high yield from the Si+N₂O→SiO+N₂ reaction. The energy stored in the triplet states is transferred in a highly efficient collisional process to pump sodium atoms to their lowest excited 3d² D, 4d²D, and 5s²S states. Adopting a sequence in which high concentrations of silicon and sodium atoms are mixed and oxidized, a continuous amplification (gain condition) is monitored which suggests the creation of a population inversion among the receptor sodium-atom energy levels and forms the basis for full cavity oscillation on the Na4 d²D-3p²P transition at 569 nm     

Regular VLSI architectures for multiplication modulo(2n+1)

The authors describe VLSI architectures for multiplication modulo p, where p is a Fermat prime. With increasing p , ROM-based table lookup methods become unattractive for integration due to excessive memory requirements. Three novel methods are discussed and compared to ROM implementations with regard to their speed and complexity characteristics. The first method is based on an ( n+1)×(n+1)-bit array multiplier, the second on modulo p carry-save addition, and the third on modulo (p -1) carry-save addition using a bit-pair recoding scheme. All allow very high throughputs in pipelined implementations. While the former is very convenient for CAD (computer-aided design) environments providing a pipelined multiplier macrocell, the latter two are well-suited to full-custom implementation     

Pseudocyclic maximum-distance-separable codes

The (n, k) pseudocyclic maximum-distance-separable (MDS) codes modulo (xⁿ- a) over GF(q) are considered. Suppose that n is a divisor of q+1. If n is odd, pseudocyclic MDS codes exist for all k. However, if n is even, nontrivial pseudocyclic MDS codes exist for odd k (but not for even k) if a is a quadratic residue in GF(q), and they exist for even k (but not for odd k) if a is not a quadratic residue in GF(q). Also considered is the case when n is a divisor of q-1, and it is shown that pseudocyclic MDS codes exist if and only if the multiplicative order of a divides (q-1)/n, and that when this condition is satisfied, such codes exist for all k. If the condition is not satisfied, every pseudocyclic code of length n is the result of interleaving a shorter pseudocyclic code     

Reliability of a consecutivek-out-of-r-from-n:F system

The reliability of the consecutive k-out-of-r-from-n:F system is studied. For k=2 an explicit solution is given for n components in line or in cycle in the i.i.d. case. For k⩾3 sharp lower and upper bounds are given for the reliability of the system and demonstrated for different values of n, k, r, p. These bounds are exact for r=n, n-1, n-2, n-3, and for these values the exact analytic solution is also given     

On the decoding of algebraic-geometric codes

A decoding algorithm for algebraic-geometric codes arising from arbitrary algebraic curves is presented. This algorithm corrects any number of errors up to [(d-g-1)/2], where d is the designed distance of the code and g is the genus of the curve. The complexity of decoding equals σ(n³) where n is the length of the code. Also presented is a modification of this algorithm, which in the case of elliptic and hyperelliptic curves is able to correct [(d-1)/2] errors. It is shown that for some codes based on plane curves the modified decoding algorithm corrects approximately d/2-g/4 errors. Asymptotically good q-ary codes with a polynomial construction and a polynomial decoding algorithm (for q⩾361 on some segment their parameters are better than the Gilbert-Varshamov bound) are obtained. A family of asymptotically good binary codes with polynomial construction and polynomial decoding is also obtained, whose parameters are better than the Blokh-Zyablov bound on the whole interval 0<σ<1/2     

High-speed Ga0.47In0.53As/InP infra-redSchottky-barrier photodiodes

The authors report a new high-speed InP-based Ga_1-xIn _xAs infra-red Schottky-barrier photodiode. The photodiodes were fabricated on both p- and n-GaInAs epilayers using Schottky barrier height enhancement technology. The response speed was measured by the impulse response and autocorrelation method; the risetimes of 85 ps for p-GaInAs and 180 ps for n-GaInAs photodiodes were obtained, which correspond to the 3 dB cutoff frequency of 2-4 GHz. The intrinsic response speed was 12 GHz for n-GaInAs and 18 GHz for p-GaInAs photodiodes based on SPICE simulation with measured device parameters. The photodiodes had the responsivity as high as 0.55 A/W and the quantum efficiency of up to 45% at 1.3-1.6 μm without antireflection coating     

Tight bounds on the redundancy of Huffman codes

A method for deriving optimal upper bounds on the redundancy of binary Huffman codes in terms of the probability p₁ of the most likely source letter is presented. This method will be used to compute bounds for all p₁⩾1/127, which were previously known only for a few special cases. Furthermore, the known optimal lower bound for binary Huffman codes is generalized to arbitrary code alphabets and some upper bounds for D-ary Huffman codes, 2⩽D<∞, are given, which are the tightest possible for all p₁⩾1/2     

Polyspectrum modeling using linear or quadratic filters

The polyspectrum modeling problem using linear or quadratic filters is investigated. In the linear case, it is shown that, if the output pth-order cumulant function of a filter, driven by a white noise, is of finite extent, then the filter necessarily has a finite-extent impulse response. It is proved that every factorable polyspectrum with a non-Gaussian white noise can also be modeled with a quadratic filter driven by a Gaussian white noise. It is shown that, if the quadratic filter has a finite-extent impulse response, then the output pth-order cumulant function is of finite extent; and if the output pth-order cumulant function of a quadratic filter is of finite extent, then the impulse response may or may not be of finite extent. It is shown that there exist finite and infinite extent p th-order cumulant functions that are not factorable but can be modeled with quadratic filters     

Binary linear quasi-perfect codes are normal

Whether quasi-perfect codes are normal is addressed. Let C be a code of length n, dimension k, covering radius R, and minimal distance d. It is proved that C is normal if d⩾2R-1. Hence all quasi-perfect codes are normal. Consequently, any [n,k ]R binary linear code with minimal distance d⩾2R-1 is normal     

Phase tree: a periodic, fractional flux quantum vernier forhigh-speed interpolation of analog-to-digital converters

A Josephson junction circuit that can rapidly track and record a magnetic flux signal to a small binary fraction of the flux quantum is proposed. This so-called phase tree circuit behaves periodically, recording the residue of the signal modulo the flux quantum in 2^p ths of a flux quantum for a p-level binary tree. Signal quantization is accomplished by comparators that read the 2^p-1 circulating currents in the leaf-level branches, providing a total of 2^p possibilities in the periodic code. The phase tree can therefore be used as a vernier, linear over a large number of periods because a single analog element determines the quantization levels once the network is properly biased. A system consisting of a conventional m-bit analog-to-digital converter (ADC m≈4-7) and an auxiliary p-bit phase tree interpolator (p≈2-5) can achieve at least m+p -1 bits without loss of bandwidth or sample rate     

Distributed fiber-optic interferometric sensor for the detection ofpressure fluctuations in reservoirs

A fiber-optic interferometric sensor for the detection of the resonant modes of reservoirs is reported. Study of the characteristics of fiber-optic hydrophones identified the ratio ΔL/Δp, i.e., the differential fiber-optic elongation due to pressure change, as the critical parameter to be enhanced in order to improve the sensor sensitivity. A model of the sensor, suitable for detecting the very-low-frequency and long-wavelength pressure changes characteristic of reservoir resonances, is proposed. The sensor is designed as a straight length of optical fiber with small masses attached at regular intervals. The dynamical analysis shows a sensitivity two orders of magnitude larger than that of the unmodified optical fiber. Use of the sensor as a resonant device is discussed. Experiments performed using the first prototype in a resonant tank are described and agree well with theoretical predictions, confirming the validity of the approach     

Constructions of error-correcting DC-free block codes

Two DC-free codes are presented with distance 2d, b ⩾1 length 2n+2r(d-1) for d⩽3 and length 2n+2r(d-1)(2d -1) for d>3, where r is the least integer ⩾log₂ (2n+1). For the first code l=4, c=2, and the asymptotic rate of this code is 0.7925. For the second code l=6, c=3, and the asymptotic rate of this code is 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes do not achieve the best rate. As an example of codes of short length with good rate, the author presents a (30, 10, 6, 4) DC-free block code with 2²¹ codewords. A construction is presented for which from a given code C ₁ of length n, even weight, and distance 4, the author obtains a (4n, l, c, 4) DC-free block code C₂, where l is 4, 5 or 6, and c is not greater than n+1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. The encoding and decoding procedures for all the codes are discussed     

Code division multiple-access techniques in optical fiber networks.I. Fundamental principles

An examination is made of fiber-optic code-division multiple-access (FO-CDMA), a technique in which low information data rates are mapped into very-high-rate address codes (signature sequences) for the purpose of achieving random, asynchronous communications free of network control, among many users. The need for a special class of signature sequences to achieve the multiple-access capability using fiber-optic signal processing techniques is discussed. A class of signature sequences called optical orthogonal codes (OOCs) that provide the auto- and cross-correlation properties required for FO-CDMA is introduced and used in an experiment to show the principles of FO-CDMA. The experiment demonstrates the auto- and cross-correlation properties of the codes. The concept of optical disk patterns, an equivalent way of representing the OOCs, is introduced. The patterns are used to derive the probability density functions associated with any two interfering OOCs. A detailed study of different interference patterns is presented, and the strongest and the weakest interference patterns are determined     

A note on D-ary Huffman codes

An upper bound on the redundancy of D-ary Huffman codes in terms of the probability p₁ of the most likely source letter is provided. For large values of p₁, the bound improves the one given by R.G. Gallager (1978). Additionally, some results known for the binary case (D=2) are extended to arbitrary D-ary Huffman codes. As a consequence, a tight lower bound that corrects a bound recently proposed by J.D. Golic and M.M. Obradovic (1987) is derived     

On the existence of optimum cyclic burst correcting codes over GF(q)

A cyclic b-burst correcting code over GF(q) of redundancy r and length n=(q^r-b+1-1)/(q-1) is said to be optimum. It is proved that a necessary condition for the existence of such a code is the existence of a square-free polynomial in GF(q)[x] of degree b-1 which is not divisible by x such that its period and the degrees of its irreducible factors are relatively prime to q-1. Moreover, if such a polynomial exists, then there are an infinite number of optimum cyclic b-burst correcting codes over GF(q)     

Rate-compatible punctured convolutional codes (RCPC codes) andtheir applications

The concept of punctured convolutional codes is extended by punctuating a low-rate 1/N code periodically with period P to obtain a family of codes with rate P/(P+l), where l can be varied between 1 and (N-1)P. A rate-compatibility restriction on the puncturing tables ensures that all code bits of high rate codes are used by the lower-rate codes. This allows transmission of incremental redundancy in ARQ/FEC (automatic repeat request/forward error correction) schemes and continuous rate variation to change from low to high error protection within a data frame. Families of RCPC codes with rates between 8/9 and 1/4 are given for memories M from 3 to 6 (8 to 64 trellis states) together with the relevant distance spectra. These codes are almost as good as the best known general convolutional codes of the respective rates. It is shown that the same Viterbi decoder can be used for all RCPC codes of the same M. the application of RCPC codes to hybrid ARQ/FEC schemes is discussed for Gaussian and Rayleigh fading channels using channel-state information to optimise throughput     

Explicit formulas for self-complementary normal bases in certainfinite fields

Explicit formulas are given for sets of p elements forming a self-complementary normal basis of GF(q^p) over GF(q), where p is the characteristic of GF(q ). Using these formulas, a straightforward construction of self-complementary bases for GF(q^α) (where α=p^m) over GF(q) is also presented     

Frequency-hopping code sequence designs having large linear span

In frequency-hopping spread-spectrum multiple-access communication systems, it is desirable to use sets of hopping patterns that, in addition to having good Hamming correlation properties and large period, are also derived from sequences having large linear span. Here, two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented. The Hamming correlation properties of the designs are optimal in the first case and close to optimal in the second. In terms of the alphabet size p (required to be prime in both cases), the period and family size of the two designs are given by (p², p) and (p ⁿ, p^n/2+1) (n an even integer), respectively. The finite field sequences underlying the patterns in the first design have linear span exceeding p, whereas still larger linear spans (when compared to the sequence period) can be obtained using the second design method     

The pi-persistent protocol for unidirectionalbroadcast bus networks

A protocol for multiaccess communication over unidirectional bus networks is proposed, and its performance capabilities are determined. Under this protocol, time is slotted with a slot equaling a packet's transmission time. A station with a packet to send persists in transmitting its packet in an empty slot with probability p_i until it is successful. Three criteria for fairness in selection of the p_i are modeled using Markov chains, which are solved to obtain the proper p_i that satisfy each fairness criterion. Unlike previous studies of unidirectional bus networks, stations are allowed to buffer more than one packet. The average packet delay for this protocol is bounded, and the maximum achievable throughput approaches unity with increasing buffer size. Further, the protocol provides better delay versus throughput behavior for fixed packet lengths than previous round-robin schemes, its performance is insensitive to bus characteristics, and it appears to be particularly well suited for fiber-optic network applications requiring long distances and high bandwidths. Simulation results that confirm the predicted performance are included