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     

Improved sphere bounds on the covering radius of codes

The sphere bound is a trivial lower bound on K(n,R), the minimal cardinality of any binary code of length n and with covering radius R. By simple arguments it is considerably improved, to K(n,1)⩾2 ⁿ/n for n even. A table of lower and upper bounds on K(n,R) for n⩽33, R ⩽10 is included     

A convolutional single-parity-check concatenated coding scheme forhigh-data-rate applications

The coding scheme uses a set of n convolutional codes multiplexed into an inner code and a (n,n-1) single-parity-check code serving as the outer code. Each of the inner convolutional codes is decoded independently, with maximum-likelihood decoding being achieved using n parallel implementations of the Viterbi algorithm. The Viterbi decoding is followed by additional outer soft-decision single-parity-check decoding. Considering n=12 and the set of short constraint length K=3, rate 1/2 convolutional codes, it is shown that the performance of the concatenated scheme is comparable to the performance of the constraint length K=7, rate 1/2 convolutional code with standard soft-decision Viterbi decoding. Simulation results are presented for the K=3, rate 1/2 as well as for the punctured K=3, rate 2/3 and rate 3/4 inner convolutional codes. The performance of the proposed concatenated scheme using a set of K=7, rate 1/2 inner convolutional codes is given     

Lower bounds for q-ary covering codes

The authors prove combinatorial lower bounds for K_q (n,R), the minimal cardinality of any q-ary code of length n and covering radius R. Tables of lower bounds for K_q(n,R) are presented for q=3, 4, 5     

Optimization of signal sets for partial-response channels. II.Asymptotic coding gain

For Pt. I see ibid., vol.37, no.5, p.1327-141 (1991). For a linear, time-invariant, discrete-time channel with a given transfer function H(f), and information rate R bits/ T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2^RK inputs of length K that maximizes the minimum l₂ distance between pairs of outputs. The author studies the minimum distance between outputs, or equivalently, the coding gain of optimal signal sets as K→∞. He shows how to estimate the coding gain, relative to single-step detection, of an optimal signal set length K when K is large     

The axisymmetric modes in a longitudinal inhomogeneous SELFOC fiber

The authors consider the propagation characteristics and mode conversion of axisymmetric modes in an imperfect SELFOC fiber with longitudinal gradually varying dielectric constant K=ϵ/ϵ₀=K₀-K ₂(z)r². An analytic solution which is expressed in terms of generalized Laguerre polynomials is found     

Lower bounds for binary covering codes

G.D. Chen et al. (ibid., vol.IT-32, p.680-94, 1986) presented two new lower bounds for K(n,R), where K(n,R) denotes the minimum cardinality of a binary code of length n and covering radius R. The author shows that a slight modification gives further improvements and some examples are given to confirm the argument. Codes that have a certain partitioning property are considered     

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     

Performance analysis of RS-coded M-ary FSK forfrequency-hopping spread spectrum mobile radios

Decoding performance of Reed-Solomon (RS) coded M-ary FSK with noncoherent detection in a frequency-hopping spread spectrum mobile radio channel is theoretically analyzed. Exact formulas and an approximate one for evaluating word error rates (WERs) of error correction and error-and-erasure correction schemes on decoding the RS codes are derived. It is shown that with K symbol erasure and C symbol error detection, RS coded M-ary FSK achieves the equivalent diversity order of (K+1)(C+1)     

Dependence of nonlinear gain effect on threshold gain insemiconductor lasers-an optimization for high-speed modulation

The dependence of nonlinear gain parameter and K factor on material gain in semiconductor lasers has been investigated theoretically by calculating (dg/dS)_s=0, derivative of gain g with respect to photon density S. If spectral hole burning is assumed, the square of the line-shape function appears in dg/dS. This implies that the contributions from high-energy electron-hole pairs are reduced, and that (dg/dS)_S=0 takes a finite negative value at transparent point (g=0). The nonlinear gain parameter, therefore, diverges, as the gain approaches zero. The K factor is minimized at a value of material gain, which is estimated to be 4.3 ps^-1 for typical InGaAs/InGaAsP quantum well lasers. The confinement factor should be designed to maintain the gain at the optimum value     

Quantile estimation based on nomination sampling

Nomination sampling is a sampling process in which every observation is the maximum of a random sample from some distribution. If all samples are taken from a single underlying CDF, F, data can be viewed as consisting of pairs (X_i,K_i) where K_i is the size of sample i and, given K_i=k_i, X_i is distributed according to CDF F^ki. R.A. Boyles and F.J. Samaniego (1986) developed a nonparametric maximum-likelihood estimator of F. In the present work, their approach is extended to obtain estimates of the quantiles of F and to study the limit theory and consistency properties of these estimates. These results generalize the results of T.R. Willemain (1980), who discussed the estimation of the median of F based on nomination samples     

Asymptotically optimal classification for multiple tests withempirically observed statistics

The decision problem of testing M hypotheses when the source is Kth-order Markov and there are M (or fewer) training sequences of length N and a single test sequence of length n is considered. K, M, n, N are all given. It is shown what the requirements are on M , n, N to achieve vanishing (exponential) error probabilities and how to determine or bound the exponent. A likelihood ratio test that is allowed to produce a no-match decision is shown to provide asymptotically optimal error probabilities and minimum no-match decisions. As an important serial case, the binary hypotheses problem without rejection is discussed. It is shown that, for this configuration, only one training sequence is needed to achieve an asymptotically optimal test     

The total PFA of the multiwindow harmonicdetector and its application to real data

The authors study the multiwindow spectral analysis method as it applies to the detection of sinusoidal signals. They examine the probability of false alarm P_FA. The total P _FA (sinusoidal frequency unknown) is shown analytically to be bounded below by the order statistics (minimum) of BM/K independent identically distributed (i.i.d.) beta variates, where M is the length of the data record used in the detection, K the number of windows, and B the width of the frequency band of interest. Simulation results indicate a much larger bound, the minimum of BM i.i.d. beta variates. It is shown that for real signals, the assumptions made in the derivation of the detector break down at frequencies close to zero and to half the sampling frequency     

State-dependent routing on symmetric loss networks with trunkreservations. I

The aggregated-least-busy-alternative (ALBA), a distributed, state-dependent, dynamic routing strategy for circuit-switched loss networks is discussed. The networks considered are symmetric and fully connected. The offered calls form Poisson streams, and routes have at most two links. In ALBA(K), the states of each link are lumped into K (K⩾2) aggregates, and the route of each call is determined by local information on the aggregate states of the links of the alternate routes at the time of the call's arrival. The last aggregate is always the set of states reserved for direct traffic. A fixed-point model for ALBA(K) for general K is presented. The particular case of ALBA in which there is no aggregation is least busy alternative (LBA); ALBA(2) represents the other extreme of aggregation. Simulation and analytic results for LBA are compared. An asymptotic scaling based on the fixed-point models is also discussed. It is shown that there is a dichotomy in network behavior: if the offered traffic is below a threshold, then the network loss probability decreases exponentially with increasing network size, and above the threshold, performance is poor     

Nonparametric Bayes estimation of a distribution under nominationsampling

Nomination sampling is a sampling process in which every observation is the maximum of a random sample from some distribution. If the data are {(Y_i, K_i), i =1, . . ., n} where K_i is the size of sample i, and Y_i is the maximum of a random sample of size K_i from an unknown Cdf, F; the Bayes estimator of F is derived by discretizing F over a fixed finite partition of the support of F and taking a Dirichlet distribution as the prior for the probabilities of the partitioning intervals. For the flood data of the Nidd River considered by R.A. Boyles and F.J. Samaniego (J. Am. Stat. Assoc., vol.81, p.1039-45, 1986), the plots of the Bayes estimator of F are obtained for several sets of values of the parameters of the Dirichlet distribution     

Bounds for abnormal binary codes with covering radius one

The normality of binary codes is studied. The minimum cardinality of a binary code of length n with covering radius R is denoted by K(n,R). It is assumed that C is an (n,M)R code, that is, a binary code of length n with M codewords and covering radius R. It is shown that if C is an (n,M)1 code, then it is easy to find a normal (n ,M)1 code by changing C in a suitable way, and that all the optimal (n,M)1 codes (i.e. those for which M=K(n,1)) are normal and their every coordinate is acceptable. It is shown that if C is an abnormal (n,M) code, then n⩾9, and an abnormal (9118)1 code which is the smallest abnormal code known at present, is constructed. Lower bounds on the minimum cardinality of a binary abnormal code of length n with covering radius 1 are derived, and it is shown that if an (n,M)1 code is abnormal, then M⩾96     

High-performance self-aligned (Al,Ga)As/(In,Ga)As pseudomorphicHIGFETs

Transconductance as high as 676 mS/mm at 300 K was observed to 0.7×10-μm² n-channel devices (HIGFETs) made on epilayers with Al_0.3Ga_0.7As insulator thickness of 200 Å and In_0.15Ga_0.85As channel thickness of 150 Å. An FET K value (K=W_g Uε/2aL_g) as large as 10.6 mA/V ² was also measured from another device with transconductance of 411 mS/mm. The high K values are achieved under normal FET operation without hole-injection or drain-avalanche breakdown effects. These results demonstrate the promise of pseudomorphic (Al,Ga)As/(In,Ga)As HIGFETs for high-performance circuit applications     

Packet error probabilities in frequency-hopped spread-spectrumpacket radio networks-memoryless frequency-hopping patterns considered

The packet error probability induced in a frequency-hopped spread-spectrum packet radio network is computed. The frequency spectrum is divided into q frequency bins. Each packet is exactly one codeword from an (M, L) Reed-Solomon code [M=number of codeword symbols (bytes); L=number of information symbols (bytes)]. Every user in the network sends each of the M bytes of his packet at a frequency chosen among the q frequencies with equal probability and independently of the frequencies chosen for other bytes (i.e., memoryless frequency-hopping patterns). Statistically independent frequency-hopping patterns correspond to different users in the network. Provided that K users have simultaneously transmitted their packets on the channel and a receiver has locked on to one of these K packets, the probability that this packet is not decoded correctly is evaluated. It is also shown that although memoryless frequency-hopping patterns are utilized, the byte errors at the receiver are not statistically independent; instead they exhibit a Markovian structure     

Smaller cells for greater performance

A microcell architecture that reduces interference, increases system capacity, improves voice quality, and demands fewer handoffs is described. The system is easy to implement and poses a very low risk investment. Its capacity and voice quality are analyzed. Capacity, based on the K=3 system (K is the cell reuse factor), is 2.33 times higher than the existing analog system of K=7. This microcell system can provide better voice quality than the Advanced Mobile Phone Service (AMPS) cellular system at 850 MHz. It can be used with digital cellular with slight modification, and is suitable for in-building communications     

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