The performance of coded multi-pulse pulse position modulation (MPPM) consisting of m slots and 2 pulses, denoted as (m, 2) MPPM, with imperfect slot synchronization is analyzed. Convolutional codes and Reed-Solomon (RS) codes are employed for (m, 2) MPPM, and the bit error probability of coded (m, 2) MPPM in the presence of the timing offset is derived. In each coded (m, 2) MPPM, we compare the performance of some different code rate systems. Moreover, we compare the performance of both systems at the same information bit rate. It is shown that in both coded systems, the performance of code rate-1/2 coded (m, 2) MPPM is the best when the timing offset is small. Wheji the timing offset is somewhat large, however, uncoded (m, 2) MPPM is shown to perform better than coded (m, 2) MPPM. Further, convolutional coded (m, 2) MPPM with the constraint length k7 is shown to perform better than RS coded (m, 2) MPPM for the same code rate.

A permutation cipher scheme using polynomials over a field is presented. A permutation as well as substitution plays a major role in almost all conventional cryptosystems. But the security of the permutation depends on how symbols are permuted. This paper proposes the use of polynomials for the permutation and show that the scheme satisfies the following security criteria. (1) There are enough encryption keys to defend exhaustive attacks. (2) The permutation moves almost all samples into places which are different from the original places. (3) Most samples are shifted differently by different permutations. The permutation cipher scheme could be regarded as a scheme based on Reed-Solomon codes. The information symbols of the codes compose a key of the permutation cipher scheme.

Coding scheme is discussed for M-Choose-T communication in which at most T active users out of M potential users simultaneously transmit their messages over a common channel. The multiple-access channel considered in this paper is assumed to be a time-discrete noiseless adder channel without feedback with T binary inputs and one real-valued output, and is used on the assumption of perfect block and bit synchronization among users. In this paper a new class of uniquely decodable codes is proposed in order to realize error-free M-Choose-T communication over the adder channel described above. These codes are uniquely decodable in the sense that not only the set of active users can be specified but also their transmitted messages can be recovered uniquely as long as T or fewer users are active simultaneously. It is shown that these codes have a simple decoding algorithm and can achieve a very high sum rate arbitrarily close to unity if exactly T users are active.

The performance of parallel combinatory spread spectrum (PC/SS) communication systems in the frequency-nonselective, slowly Rayleigh fading channel is studied. Performance is evaluated by symbol error rate using numerical computation. To overcome the performance degradation caused by fading, we also studied the effects of selection diversity and Reed-Solomon coding applied to the PC/SS system. As a result, a remarkable improvement in error rate performance is achieved with Reed-Solomon coding and diversity technique. The coding rate for the maximum coding gain is almost a half of that in the additive white gaussian noise channel.

In this letter, a generalized syndrome polynomial is proposed from which several decoding key-equations for Reed-Solomon codes can be derived systematically. These equations are always solved by the extended Euclidean algorithm.