## 1 Introduction
A detailed examination of relay proximity links and networks, where both proximity hardware and networking scenarios was addressed. A strategy for secure data correspondence between the smart city's vehicular nodes, which uses the fundamentals of Elliptic Curve Cryptography (ECC) for key agreement and satellite communication for the transmission of messages over vehicles is proposed by [PERSON] and [PERSON] [28]. [PERSON] et al. [29] presented a method to recognize received signal characteristics using a hierarchical classification in a multi-layer perceptron neural network. The experiments were described where a real-time video stream transmitted in the direct broadcast satellite was utilized with several modulation types of radio frequency interference. In [30], a routing algorithm to solve the link congestion problem caused by the limited topology in a topology-inhomogeneous Low Earth Orbit (LEO) satellite navigation augmentation network was proposed and a congestion avoidance routing model for the topology-inhomogeneous LEO satellite navigation augmentation network was established. Important restrictions on the control performance are imposed by communication constraints. In [21], communication constraints were taken into account in the sense of the radio signal fading with increasing the inter-satellite distance. This leads to the space limitation within which the position of neighboring vehicles can be transmitted between them and, consequently, to reducing the number of satellites that are available for navigation data exchange. However the limitations on the transmission rate are not taken into account both in [21] and in the other above mentioned papers. It is worth noting that in practice the data transmission rate over the communication channels is always limited and, moreover, its minimization is highly useful from an energy consumption viewpoint. Among other things, decreasing the data transmission rate for the given power consumption can make it possible to increase the power of transmitted signals, expanding the area of inter-satellite interaction. The present paper is focused on the reduction of the inter-satellite demanded communication channel capacity taking into account dynamics of the satellite's relative motion and possibility of erasing the navigation data in the channel. The limitations of control under constraints imposed by the limitations of the communication channel capacity, have been deeply studied within the control theoretic literature, see [31; 32; 33; 34; 35] and the references therein. A fundamental result establishing the smallest value for which the stabilization (estimation) problem for linear time invariant (LTI) systems is obtained by [PERSON] and [PERSON] [31] and presented in the form of the seminal Data Rate Theorem. However, the study of the application control problems in aerospace under communication constraints is still very limited. In the present paper, a system of two coupled satellites is considered. As in [21], the satellites are assumed to be launched at the starting time in accordance to the specified separation conditions. It is assumed that the satellites move in a low circular near-Earth orbit and are controlled using the aerodynamic drag force, which is achieved by rotating the satellite relative to the incoming flow using a flywheel attitude control system. The main focus of the paper is in the navigation data exchange between the satellites to be used to keep the satellite motion in a swarm. To this end, the adaptive coding procedure is proposed and is studied for the cases of ideal and erasure communication channel. The regulation time is taken as the performance criterion, and its dependence on the data transmission rate is numerically studied. The reminder of the paper is organized as follows.