Several constructions are presented by which spherical codes are generated from groups of binary codes. In the main family of constructions the codes are generated from equally spaced symmetric pointsets on the real line. The main ideas are code concatenation and set partitioning. Extensive tables are presented for spherical codes in dimension n/spl les/24.>

We consider the problem of simultaneous identification and transmission of information by means of superimposed codes. It is assumed that a total population of T users share a common channel. At each time at most in of the T users are active. The output from the channel is the modulo-2 sum of the binary codewords transmitted by the active users, possibly disturbed by errors. A superimposed code is actually a set of codes-one for each user-designed in such a way that both the (at most) m active users and their messages can be identified, even in the presence of a permissible number of errors in the channel. We give several explicit constructions for superimposed codes and analyze in detail their performance. In several of the cases under study we offer codes that are proved to be best possible.>

The authors introduce the concept of superimposed codes in Euclidean n-space R/sup n/. An asymptotic existence bound is derived for such codes; the proof uses the idea of random coding. In particular, the asymptotic properties of long codes are studied. It is shown that the derived existence bound differs only by a factor of four from a nonexistence bound obtained by a simple sphere-packing argument.>

Using the Goppa codes as outer codes in a construction devised by Kautz and Singleton, an improvement of the Gilbert bound for constant weight codes is obtained.

Jamming is studied as a game in the binary adder channel. The legal user controls simultaneously the encoder and the decoder by the choice of a key; the jammer controls the channel by the choice of an interference signal. For any given pair of encoder and decoder, this leads to a two-person zero-sum game. It is shown that this game can be solved in many cases of interest. In particular, an exact measure of performance is derived for the class of so-called direct sequence systems.

Random codes for the arbitrarily varying channel are investigated. The code ensemble is restricted to increase only exponentially with codeword length; a quantity called key rate is used as a measure of the rate of increase. The reliability function for such codes is related to the reliability function for codes with unlimited key rate. Explicit results are obtained in some examples of practical interest.

Slepian's idea of group codes for analog channels is adapted to the case of antijamming codes. The main result is a codeword error probability characterized by a min-max theorem. The result is illustrated by the special cases of frequency hopping (FH) and direct sequence (DS).

The encoding of a discrete memoryless multiple source\{( X_{i}, Y_{i})\}_{i=1}^{\infty}for reconstruction of a sequence\{Z_{i}\}_{i=1}^{\infty}}, withZ_{i} = F( X_{i}, Y_{i}); i = 1,2, \cdotsis considered. We require that the encoding should be such that\{X_{i}\}_{i=1}^{\infty}is encoded first without any consideration of\{Y_{i}\}_{i=1}^{\infty}, while in a second part of the encoding, this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special caseH( X_{i}|Z_{i}, Y_{i}) = 0. Comparisons with the Slepian-Wolf problem and the Ahlswede-Korner-Wyner side information problem are carried out.

Linear periodically time-varying filters are considered as modulators and demodulators for the transmission of analog information over a stationary Gaussian channel. A complete analysis is carried out based on a certain general decomposition of such a filter into a number of branches, each containing a linear time-invariant filter and a multiplication with a complex sinusoid. Receiver optimization is carried out under the assumption that the above decomposition is finite. Finally, a joint optimization of transmitter and receiver is derived under the further restriction that the message signal is strictly band-limited.

A special case of two-way communication is considered. Two memoryless channels are used. The forward channel carries questions, generated by a memoryless source. Each question specifies a component of a vector, generated by a memoryless vector source. The value of that component is transmitted to the requesting party via the backward channel. The goal is to minimize the capacity required in the backward channel when the information rate in the forward channel is given. The result is formulated as a coding theorem stating the necessary and sufficient capacity of the backward channel when all possible questions are equally likely and the components of the above mentioned vector are independent stochastic variables with equal entropy. Some explicit codes are also derived. The rates of these codes are close to the necessary minimum. The nonsymmetric case where the questions have unequal probability and the vector components have unequal entropy is reformulated as a source coding problem.

Transmission of a time-discrete message over a time-continuous channel is considered. The channel is assumed to be stationary and Gaussian. The following results are shown. 1) An optimum receiver will always contain a matched matrix filter followed by a sampling unit. 2) Jointly optimized transmitting and receiving filters will always be strictly band limited to a set of Nyquist domains. It is shown that both these results are true for any kind of message and under any measure of performance. On the basis of these results a general time-discrete matrix channel equivalent to the original time-continuous scalar channel is derived. The significance of the results is that any optimization of transmitter and receiver is reduced from a time-continuous problem to a time-discrete one.

A hybrid digital transmission system of the kind originally proposed by Chang and Freeny [4], [6] is considered. Based on predictions about cable and repeater costs around 1980, an investigation of a certain economic measure of goodness is performed. Specifically, the influence on the system cost of the choice of certain fundamental system parameters like repeater spacing, symbol rate, and number of signal levels is studied.

Joint optimization of transmitting and receiving filters in pulse-amplitude-modulated stationary Gaussian channels has been considered by a large number of authors under a variety of different circumstances. In most cases it has been found that the optimum filters are strictly band limited. In the present correspondence we give a direct argument why this must be so for a broad class of joint optimization problems.

It has been observed by several authors that a number of different optimum receiving filters (corresponding to different criteria of goodness) for sampled-data transmission systems can be factored as a product of a matched filter and a periodic filter with the period equal to the sampling frequency. By a simple argument it is shown in this correspondence that any reasonable criterion of goodness will lead to an optimum filter that has this form.

An interleaved fading channel whose state is known to the receiver is analyzed. The reliability functionE(R)is obtained for ratesRin the rangeR_c \leq R \leq C. The capacity is shown to beC = E_A \{ \frac{1}{2} \ln (1 + A^2 n)\}whereAis a factor describing the fading mechanism anduis the signal-to-noise ratio per dimension.