Recently, the low earth orbit satellite communications has been attracting much attention. These communications have many strong features, however, the communication performances are influenced by carrier frequency offset (CFO) and, particularly, it is hard to acquire the synchronization. A large number of publications have so far been made on the synchronization acquisition of DS/SS systems under CFO and most of them make use of the maximum likelihood decision in finding the maximum values of Fourier transform outputs. However, the implementations of Fourier transforms usually require high cost and large space. In this paper, we propose a new simple acquisition scheme using half-symbol differential decoding technique for DS/SS systems under CFO. This scheme makes use of the addition and subtraction of baseband signals and their delayed versions, (omitting Fourier transforms), together with integrations by recursive integrators, and thus resulting in much simpler implementation. In general, it is shown that the proposed scheme can acquire the code synchronization under carrier frequency offset with much smaller computational complexities and the sacrifice of longer acquisition time.

M-ary orthogonal keying (MOK) systems under carrier frequency offset (CFO) are investigated. It is shown that spurious signals are introduced by the offset frequency components of spectrum after multiplication in correlation detection process, and some conditions on robust orthogonal signal sets are derived. Walsh function sets are found to be very weak against CFO, since they produce large spurious signals. As robust orthogonal signal sets against CFO, the rows of circulant Hadamard matrices are proposed and their error performanses are evaluated. The results show that they are good M-ary orthogonal signal sets in the presence of CFO.

It is well known that M-ary/spread spectrum (M-ary/SS) system is superior to direct-sequence spread spectrum system under AWGN, and can achieve high spectral efficiency. On the other hand, however, the main drawback of this system is that the synchronization acquisition is difficult. In this paper, we propose a new synchronization acquisition method of M-ary/SS system. This method acquires the code synchronization by introducing a symmetrical property in spreading sequences, and detecting this property with the differential decoding technique. As spreading sequences, a set of orthogonal sequences and a set of non-orthogonal sequences are considered. The strong features of proposed systems are that the systems can acquire the code synchronization in carrier band and can reduce the complexity of calculation greatly. Among the comparison results of the systems with newly proposed orthogonal and some specific non-orthogonal spreading sequences, it is especially noted that the latter can reduce the mean acquisition time and calculation complexity much greater than the former.

Even though coding theory applications in fault tolerant computing started with Hamming code invention, their developments were made almost independently from those in information and communication theories after this initiation. This paper gives a brief overview on coding theory applications in fault tolerant computing. A more detailed survey was made on the most important recent developments. Since there are many items of mutual interest to engineers in both fields, mutual stimulations and cooperations between them would be highly appreciated for future mutual developments in coding theory applications.