Bit error rate (BER) performance of convolutional coding/soft decision Viterbi decoding is investigated theoretically. Firstly, equations are derived to calculate the tight upper bound of the BER performance for the multi-level soft decision with arbitrary threshold spacing, considering the quantized metric used in the Viterbi decoder. Experimental results on the BER performance of a rate 1/2 code with constraint length 7 are shown to demonstrate that the derived equations provide the precise BER performance. Then, the BER performance of various codes is calculated for 4- and 8-level soft decision as well as hard decision and ideal (infinite level) soft decision. The codes examined in this paper cover typical codes with 64 states of rate 1/4 through 3/4 and the rate 1/2 codes with constraint length 3 through 14. From the BER curves obtained for these codes, the coding gain is clarified as a function of coding rate and code constraint length. Main results obtained in this paper are as follows. (1) Among codes with 64 states, rate 1/3 code gives the maximum coding gain. (2) Coding gain of a rate 1/2 code increases as constraint length K becomes large. In the case of 8-level soft decision, for instance, the coding gain of the code with K14 reaches 7.1 dB at BER10-6, which is close to the maximum coding gain obtained by an infinite constraint length code (estimated to be 7.9 dB).

The problems of robust tracking with stability for uncertain plants are considered. Uncertrain plants of one type are systems whose transfer matrices are only known to belong to a convex hull of prescribed transfer matrices P1, P2,, PN . Such uncertain systems include some dynamical interval systems as examples. A necessary and sufficient condition for the solvability is represented in terms of extreme points P1, P2,, PN of the convex hull. The solvability condition is testable and leads to a systematic procedure for designing a robust feedback control system.

Since the first use of mobile satellite communications in 1976 by MARISAT, a number of studies have been carried out to expand their application from international to regional, and to domestic services. By employing the conventional satellites for fixed satellite communications, domestic mobile satellite data communication services have been in commercial use since 1989. Moreover, domestic mobile satellite communication systems employing dedicated satellites to mobile satellite communication are scheduled for commercial operation in Australia, Canada and the USA. Prior to this operation, preliminary mobile satellite communications services employing the MARISAT and MARECS B-2 satellites for data transmission started in Canada and the USA in 1990. Furthermore, more sophisticated and advanced mobile satellite communication systems such as personal communication systems are under development in various countries. This paper reviews the current and future mobile satellite communication systems and related technologies.