Gray codes, where two consecutive codewords differ in exactly one position by plusmn1, are given. In a single radix code, all dimensions have the same base, sayk, whereas in a mixed radix code the base in one dimension can be different from the base in another dimension. Constructions of new classes of mixed radix Gray codes are presented. It is shown how acyclicmixedradixGraycodecorresponds to a Hamiltonian cycle in a mixed radix toroidal graph. It is then shown how these codes can be used as a basis for constructing edge disjoint Hamiltonian cycles in mixed radix toroidal networks when the number of dimensions, n = 2rfor some r ges 0.

Gray codes, where two consecutive codewords differ in exactly one position by plusmn1, are given. In a single-radix code, all dimensions have the same base, say, kappa, whereas, in a mixed-radix code, the base in one dimension can be different from the base in another dimension. Constructions of new classes of mixed-radix Gray codes are presented. It is shown how these codes can be used as a basis for constructing edge-disjoint Hamiltonian cycles in mixed-radix toroidal networks when the number of dimensions n = 2rfor some r ges 0. Efficient algorithms for the generation of these codes are then shown.

Forward error control (FEC) and automatic-repeat request (ARQ) is two main techniques used for reliable data transmission in computer and communication systems. In this paper, some simple, low cost error control techniques for ARQ protocols used with binary unidirectional channels are described. The proposed schemes can correct up to [t/2] unidirectional errors using t-unidirectional error detecting codes and code combining with a much smaller number of retransmissions. First, we show how to do code combining for unidirectional errors. To use code combining with unidirectional codes, we need to identify the type of error (0rarr1 or 1rarr0) from the received word. We show how this can be done for various unidirectional codes

Forward error control (FEC) and automatic-repeat request (ARQ) are two main techniques used for reliable data transmission in computer and communication systems. In this paper, some simple, low cost error control techniques for ARQ protocols used with binary unidirectional channels, are described. The proposed schemes can correct up to [t/2] unidirectional errors using t-unidirectional error detecting codes and code combining with much less number of retransmissions. First we show how to do code combining for unidirectional errors. To use code combining with unidirectional codes, we need to identify the type of error (0 rarr 1 or 1 rarr 0) from the received word. We show how this can be done for various unidirectional codes