A neural network model based on pulse signals is presented. Pulsed signals are shown to give the model such properties as a simplified hardware implementation, the ability to use stochastic search techniques, and biological plausibility. In this model, there is also the possibility of building modular neural systems. Since information representation in pulsed signals has to be studied carefully, the stochastic representation is outlined and it is shown how generation of a signal and estimation of information are obtained. Several design issues have to be solved before it is possible to use a model of this kind, and solutions are proposed for synaptic multiplication, summation, and nonlinearity. It is also shown that reinforcement learning is the type of learning which is best suited for this type of model and that this does not interfere with the properties mentioned above. Initial simulations of the model show promising results

Permutation modulation is a class of group codes for the Gaussian channel. A group code is a set of vectors obtained by a group of orthogonal matrices operating on an initial vector. An important problem is to find the initial vector yielding the largest minimum Euclidean distance between two vectors. This problem is solved for permutation modulation. The performance of such optimized permutation modulation is analyzed. Compared to binary antipodal signals and PSK (phase-shift keying), it typically requires 2.5-4 dB less energy for the same minimum distance.>

Encryption is used in a communication system to safeguard information in the transmitted messages from anyone other than the intended receiver(s). To perform the encryption and decryption the transmitter and receiver(s) ought to have matching encryption and decryption keys. A clever way to generate these keys is to use the public key distribution system invented by Diffie and Hellman. That system, however, admits only one pair of communication stations to share a particular pair of encryption and decryption keys, The public key distribution system is generalized to a conference key distribution system (CKDS) which admits any group of stations to share the same encryption and decryption keys. The analysis reveals two important aspects of any conference key distribution system. One is the multitap resistance, which is a measure of the information security in the communication system. The other is the separation of the problem into two parts: the choice of a suitable symmetric function of the private keys and the choice of a suitable one-way mapping thereof. We have also shown how to use CKDS in connection with public key ciphers and an authorization scheme.

Encryption is an efficient method for information protection in communication links which are subject to wiretapping. In this paper we discuss the application of encryption to satellite communication systems in which the satellite has on-board processing capability. The on-board processor can be used in the key distribution process. Two examples of such processes are described. The first requires the storage in the satellite of one key for each user of the communication system. These are used together with a conventional encryption algorithm (DES, for example) to distribute communication keys to the users. The communication keys are then used to encrypt and decrypt information. The other key distribution process utilizes a trap-door one-way function, whose inverse is implemented in the satellite. The need for storage space in the satellite is smaller than that with the first method.

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.

A functionf(x)is chosen from a finite set of functions\cal F. An outsider observer knows\cal Fbut not the actual choicef(x). He is, however, able to make a limited number of observations(x,y)satisfying the unknown functiony = f(x). The uncertainty of the outside observer with respect to the unknown function is measured as the entropy of the output variableywhen the functionf(x)is regarded as a random choice in\cal F. With this measure, an upper bound on the uncertainty is derived. The existence of unknown functions satisfying this bound is investigated, and necessary and sufficient conditions are derived. The problem is shown to be closely related to the problem of finding algebraic codes with high minimum Hamming distance. The theory can be applied to cryptography, identifying mechanisms, access control in computers, and possibly also to reliability analysis.

A class of codes for the Gaussian channel is analyzed. The code class is a subclass of the group codes for the Gaussian channel described by Slepian. Using the vector model for the Gaussian channel, the code vectors are obtained by transformations of an initial vector. The class of codes in which the transformations form a commutative group is called the class of commutative group codes. The performance of the codes is evaluated using the union bound on the error probability as a performance measure. The union bound is shown to be closely related to the moments of the scalar product between the code vectors. Commutative group codes are described. It is shown that linear algebraic codes may be represented as commutative group codes. The code class is also shown to include simplex and biorthogonal codes in all dimensions.