Combined coded/multi-h CPFSK signaling

A continuous-phase frequency-shift-keying (CPFSK) signaling technique is suggested that combines convolutional encoding and multi- h signaling. In contrast to regular multi-h signaling, this technique changes the modulation index in a preselected pattern in order to maximize the minimum Euclidean distance. A rate-1/2 convolutional encoder along with a 2-h quaternary CPFSK modulator which uses two fixed modulation indexes is considered. Minimum Euclidean distances are calculated corresponding to the best encoder/mapper combinations for different modulation index patterns at attractive pairs of modulation indexes. Numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum Euclidean distance of coded CPFSK signals can be significantly increased by combining with multi-h signaling. Modulation index patterns which perform significantly better than regular multi-h signals are determined. An error event analysis over the additive-white-Gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results     

Electric fields and vector potentials of thin cylindrical antennas

The vector potential and elastic field generated by the current in a center-driven or parasitic dipole antenna that extends from z=-h to z=h are investigated for each of the several components of the current. These include sin k (h-|z|), sin k|z|-sin kh , cos kz-cos kh, and cos kz/2-cos kh /2. Of special interest are the interactions among the variously spaced elements in parallel, nonstaggered arrays. These depend on the mutual vector potentials. It is shown that at a radial distance ρ~ h and in the range -h⩽z⩽h, the vector potentials due to all four components become alike and have an approximately plane-wave form. Simple approximate formulas for the electric fields and vector potentials generated by each of the four distributions are derived and compared with the exact results. The application of the new formulas to large arrays is discussed     

Optimum parameter combinations for multi-h phase codes

It has been believed that the superiority of multi-h phase codes over constant-h continuous-phase frequency shift keying (CPFSK) schemes is based entirely on the longer temporal separation of any two signal paths. This assumption forces the number of states in the receiver to be lower bounded and requires a fast processor in the receiver. Counterexamples to this common belief are presented as well as results of a systematic search for good multi-h codes for a given bandwidth and complexity constraints. It is shown that quaternary multi-h codes exist for which the first merge of the phase paths in the phase tree is not delayed as compared to the CPFSK scheme, yet which still offer a significant coding gain over the corresponding CPFSK signals. Some quaternary and octal multi-h codes are found with large minimum distance values and a smaller number of receiver states than those known previously     

On the capacity region of the discrete additive multiple-accessarbitrarily varying channel

The discrete additive multiple-access arbitrarily varying channel (AVC) with two senders and one receiver is considered. Necessary and sufficient conditions are given for its deterministic-code average-probability-of-error capacity region under a state constraint to have a nonempty interior. In the case that no state constraint is present, the capacity region is characterized exactly. In the case of the noiseless mod-2 adder AVC using state constraint function l(s)=s and subject to a state constraint L less than or equal to 0.13616917, the capacity region is shown to be a 45-degree triangle whose legs have length 1-h(L), where h denotes the binary entropy function     

The capacity of the Kanerva associative memory

Asymptotic expressions for the capacity of an associative memory proposed by P. Kanerva (1984) are derived. Capacity is defined as the maximum number of random binary words that can be stored at random addresses so that the probability that a word is in error is arbitrarily small when it is retrieved by an n-bit address containing fewer than δn errors, δ⩽1/2. Sphere-packing arguments show that the capacity of any associative memory can grow exponentially in n at a rate of at most 1-h₂(δ), where h₂(δ) is the binary entropy function in bits. It turns out that the Kanerva associative memory achieves this upper bound when its parameters are optimally set. Thus, the capacity of the Kanerva associative memory has an exponential growth rate equal to the rate of the best information-theoretic codes, that is 1-h ₂(δ). However, the Kanerva memory achieves its exponential growth in capacity at the expense of an exponential growth in hardware     

Restoring a δ-pulse train by spectral fitting

The problem of restoring a δ-pulse train h(t ) from its bandpass filtered and noise-corrupted version is considered. A spectral fitting approach is described which fits terms of the form ρ_ke exp(-jωτk) to the estimated spectrum of h(t). This fitting problem can be efficiently solved using the FFT algorithm. The error in the estimated pulse positions is discussed by analyzing the fluctuation of the peak position of the cross correlation function. Computer simulation results are presented which indicate the validity of these calculations and analyses     

On optimum detection of linearly filtered CPM signals

A novel structure of the MLSE receiver for linearly filtered CPM (continuous phase modulation) signals is derived. It is shown that the correlator bank required in the works of Svensson (1987) can equivalently be replaced by a reduced correlator bank, preceded by a linear filter with impulse response h*(-t) [channel matched filter]. The reduced correlator bank only incorporates characteristics of the CPM signals and is independent of the channel impulse response. This implies that the complexity of the modified correlator bank depends only linearly on the channel filter impulse response length. The proposed receiver structure permits considerable complexity reduction when compared to the currently known solution     

Correlation between 1/f noise and hFElong-term instability in silicon bipolar devices

Accelerated life tests with high-temperature storage and electric aging for n⁺-p-n silicon planar transistors were carried out. Current gain h_FE increases monotonously with time during the tests, and the h_FE drift is correlated with initial measured 1/f noise in the transistors, i.e. the drift amount significantly increases with the increase of noise level. The correlation coefficient of relative drift Δh_FE /h_FE and 1/f noise spectral density S_iB(f) is far larger than that of Δ h_FE/h_FE and initial DC parameters of the transistors. A quantitative theory model for the h _FE drift has been developed and explains the h _FE drift behavior in the tests, which suggests that the h _FE drift and 1/f noise can be attributed to the same physical origin, and both are caused by the modulation of the oxide traps near the Si-SiO₂ interface to Si surface recombination. 1/f noise measurement, therefore, may be used as a fast and nondestructive means to predict the long-term instability in bipolar transistors     

On the average delay for routing subject to independent deflections

Consider a packet walking along a directed graph with each node having two edges directed out. The packet is headed towards one of N destinations, chosen according to a probability distribution p . At each step, the packet is forced to use a nonpreferred edge with some probability q, independently of past events. Using information theory and sequential analysis, it is shown that the mean number of steps required by the packet to reach the destination is roughly, at least H(p)/(1-h(q), where h is the binary entropy function and H(p) is the entropy (base two) of p. This lower bound is shown to be asymptotically achievable in the case where the packet always begins at a fixed node. Also considered is the maximum, over all pairs of nodes in a graph, of the mean transit time from one node to the other. The work is motivated by the search for graphs that work well in conjunction with deflection routing in communication networks     

The Zak transform and some counterexamples in time-frequencyanalysis

It is shown how the Zak transform can be used to find nontrivial examples of functions f, g∈L²(R) with f×g≡0≡F×G, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, k∈L²(R), h≠k, such that |h|=|k|, |H |=|K|. A similar construction is used to find an abundance of nontrivial pairs of functions h, k∈L² (R), h≠k, with |A_h |=|A_k| or with |W_h|=|W _k| where A_h, A_k and W_h, W_k are the ambiguity functions and Wigner distributions of h, k, respectively. One of the examples of a pair of h, k∈L²(R), h≠k , with |A_h|=|A_k| is F.A. Grunbaum's (1981) example. In addition, nontrivial examples of functions g and signals f₁≠f₂ such that f₁ and f₂ have the same spectrogram when using g as window have been found     

Electromagnetic scattering from an infinite elliptic metalliccylinder coated by a circular dielectric one

The scattering from an infinite elliptic metallic cylinder coated by a circular dielectric one is considered. The electromagnetic field is expressed in terms of both circular and elliptical cylindrical wave functions, which are connected with one another by well-known expansion formulas. In the special case of small h=ka/2 (a being the interfocal distance of the elliptic conductor and k the wavenumber of the dielectric coating), exact, closed-form expressions of the form S (h)=S(0)[1+g "h²+O(h⁴)] are obtained for the scattered field and the various scattering cross sections of the problem. Both polarizations are considered for normal incidence. Graphical results for various values of the parameters are given     

Bounds on maximum throughput for digital communications withfinite-precision and amplitude constraints

The problem of finding the maximum achievable data rate over a linear time-invariant channel is considered under constraints different from those typically assumed. The limiting factor is taken to be the accuracy with which the receiver can measure the channel output. More precisely, the following problem is considered. Given a channel with known impulse response h(t), a transmitter with an output amplitude constraint, and a receiver that can distinguish between two signals only if they are separated in amplitude at some time t ₀ by at least some small positive constant d, what is the maximum number of messages, N_max, that can be transmitted in a given time interval [0,T]? Lower bounds on N_max can be easily computed by constructing a particular set of inputs to the channel. The main result is an upper bound on N_max for arbitrary h(t). The upper bound depends on the spread of h(t), which is the maximum range of values the channel output may take at some time t₀>0 given that the output takes on a particular value α at time t=0. Numerical results are shown for different impulse responses, including two simulated telephone subscriber loop impulse responses     

Limiting efficiencies of burst-correcting array codes

The author evaluates the limiting efficiencies e(-S ) of burst-correcting array codes A(n₁,n₂, -s) for all negative readouts -s as n₂ tends to infinity and n₁ is properly chosen to maximize the efficiency. Specializing the result to the products of the first i primes donated by s_i (1⩽i<∞), which are optimal choices for readouts, gives the expression e(-s_i)=(2p_i+1 -2)/(2p_i+1-1) where p_i+1 is the next prime. Previously, it was known only that e(-2)⩾4/5 and e(-1)⩾2/3. This result reveals the existence of burst-correcting array codes with efficiencies arbitrarily close to 1 and with rates also arbitrarily close to 1     

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)     

On optimal signal sets for digital communications with finiteprecision and amplitude constraints

The maximum data rate that can be reliably communicated given a linear, time-invariant, dispersive channel, a receiver that samples the channel output to within an accuracy of ±d where d >0, and a transmitter with an output amplitude constraint is evaluated. For any dispersive channel the maximum rate depends on d and is finite. The transmitted waveforms must be designed so that two channel outputs associated with two distinct transmitted signals are separated in amplitude at a particular time by d. It is shown that given any channel impulse response with rational Laplace transform, there exists an optimal sets of inputs that are ±A everywhere where A is the maximum allowable amplitude. Furthermore, in any finite time interval, each input changes sign a finite number of times. If the channel impulse response is a single decaying exponential, it is shown that simple binary signaling, in which A or -A, depending on the current message bit, is transmitted during each symbol interval, maximizes the data rate     

A dispersion formula satisfying recent requirements in microstripCAD

A dispersion formula ϵ^*_eff(f)=ϵ^* -{ϵ^*-ϵ^*_eff(0)}/{1+( f/f₅₀)^m}, for the effective relative permittivity ϵ^*_eff(f) of an open microstrip line is derived for computer-aided design (CAD) use. The 50% dispersion point (the frequency f₅₀ at which ϵ^*_eff(f₅₀)={ϵ ^*+ϵ^*_eff(0)}/2}) is used a normalizing frequency in the proposed formula, and an expression for f₅₀ is derived. To obtain the best fit of ϵ ^*_eff(f) to the theoretical numerical model, the power m of the normalized frequency in the proposed formula is expressed as a function of width-to-height ratio w/ h for w/h⩾0.7 and as a function of w /h, f₅₀, and f for w/h⩽0.7. The present formula has a high degree of accuracy, better than 0.6% in the range 0.1<w/h⩽10, 1<ϵ^*⩽128, and any height-to-wavelength ratio h/λ₀     

Design of coded CPFSK modulation systems for bandwidth and energyefficiency

Consideration is given to the problems related to the design of M-ary continuous-phase frequency-shift keying (CPFSK) systems with modulation index h=J/M, combined with eternal rate r binary convolution encoders. The following questions are raised and answered: (1) how should different encoder-modulator systems be compared and how can comparable systems be recognized from the system parameters, i.e. M, h, and r?; (2) what are the limits on the information rate per unit bandwidth, versus signal-to-noise ratio, when reliable transmission is required?; (3) how does one choose the system parameters M, h, and r when the overall system has to achieve a specified performance?; and (4) how does one design the external rate r binary convolutional encoder to put in front of the M-ary CPFSK modulation system with h=J/M ? A simple approximation for the bandwidth of a CPFSK signal is given and shown to be sufficiently accurate for system design purposes. The design of the external convolutional encoder is carried out in a novel way that leads to fewer states in the combined encoder-modulator system and thus yields improved performance for a given demodulation-decoding complexity compared to previous approaches for the design of coded CPFSK systems     

Sliding block codes between constrained systems

The construction of finite-state codes between constrained systems called sofic systems introduced by R. Karabed and B. Marcus (1988) is continued. It is shown that if Σ is a shift of finite type and S is a sofic system with k/n=h(S )/h(Σ), where h denotes entropy, there is a noncatastrophic finite-state invertible code from Σ to S at rate k:n if Σ and S satisfy a certain algebraic condition involving dimension groups, and Σ and S satisfy a certain condition on their periodic points. Moreover, if S is an almost finite type sofic system, then the decoder can be sliding block     

Asymptotic distortion spectrum of clipped, DC-biased, Gaussiannoise [optical communication]

Consider a zero-mean, stationary Gaussian process g(t ), to which a large positive constant A has been added. Define a distortion process h_A(t) as equal to g(t)+A when the latter is negative and equal to zero otherwise. The author calculates the power spectrum of the process h_A(t) asymptotically as A becomes large. The results have application for estimating the nonlinear-distortion power in the recovered signal when many frequency-multiplexed subcarriers collectively modulate a laser's output power, as would be the case for CATV transmission over an optical fiber. The process h_A(t) then models the nonlinear distortion caused by occasional clipping of the DC-biased laser input