Biblio

In this paper, we address the stability problem of a noiseless linear time invariant control system over parallel Gaussian channels with feedback. It is shown that the eigenvalues-rate condition which has been proved as a necessary condition, is also sufficient for stability over parallel Gaussian channels. In fact, it is proved that for stabilizing a control system over the parallel Gaussian channels, it suffices that the Shannon channel capacity obtained by the water filling technique is greater than the sum of the logarithm of the unstable eigenvalues magnitude. In order to prove this sufficient condition, we propose a new nonlinear joint source channel coding for parallel Gaussian channels by which the initial state is transmitted through communication steps. This coding scheme with a linear control policy results in the stability of the system under the eigenvalues-rate condition. Hence, the proposed encoder, decoder and controller are efficient for this problem.

In this paper, we have considered the broadcasting of a memoryless bivariate Gaussian source over a Gaussian broadcast channel with respect to bandwidth compression. We have analysed the performance of a hybrid digital-analog (HDA) coding system in combination with joint source channel coding (JSCC) to measure the distortion regions. The transmission advantages due to the combination of both the analog and digital techniques, a class of HDA schemes that yields better performance in distortion is discussed. The performance of source and channel coding for the possible better outcome of the system is measured by employing Wyner-Ziv and Costa coding. In our model, we have considered the upper layer to be a combination of a hybrid layer in the sense of both the analog and digital processing is done. This is executed in presence of quantization error and performance of the system is measured with two conditions: 1) HDA scheme with quantization scaling factor α = 0, i.e. the input of the channel have only the analog information which is considered as the scaled quantization error βS 2) The analog information from the first layer S is suppressed by setting error scaling factor β = 0 and 3) Inclusion of recursive mode with JSCC in each of the three layers for the possible better outcome is considered here.