The performance of general binary block codes on an unquantized additive white Gaussian noise (AWGN) channel at low signal-to-noise ratios is considered. Expressions are derived for both the block error and the bit error probabilities near the point where the bit signal-to-noise ratio is zero. These expressions depend on the global geometric structure of the code, although the minimum distance still seems to play a crucial role. Examples of codes such as orthogonal codes, biorthogonal codes, the (24,12) extended Golay code, and the (15,6) expurgated BCH code are discussed. The asymptotic coding gain at low signal-to-noise ratios is also studied.>

Recently, Posner noted that on a wide-band Gaussian broadcast channel, ordinary time-shared coding performs almost as well as more sophisticated broadcast coding strategies. In this note, we shall give a quantitative version of Posner's result and argue that for certain realistic broadcast channels time sharing may suffice.

Motivated by a problem in optical communication, we consider the general problem of maximizing the entropy of a stationary random process that is subject to an average transition cost constraint. Using a recent result of Justesen and Hoholdt, we present an exact solution to the problem and suggest a class of finite state encoders that give a good approximation to the exact solution.

Upper bounds On the decoder error probability for Reed-Solomon codes are derived. By definition, "decoder error" occurs when the decoder finds a codeword other than the transitted codeword; this is in contrast to "decoder failure," which occurs when the decoder fails to find any codeword at all. These results imply, for example, that for aterror-correcting Reed-Solomon code of lengthq - 1over GF(q), if more thanterrors occur, the probability of decoder error is less than1/t!.

Motivated by the needs of NASA's Voyager 2 mission, in this paper we describe an algorithm which detects and corrects losses of node synchronization in convolutionally encoded data. This algorithm, which would be implemented as a hardware device external to a Viterbi decoder, makes statistical decisions about node synch based on the hard-quantized undecoded data stream. We will show that in a worst-case Voyager environment, our method will detect and correct a true loss of synch (thought to be a very rare event) within several hundred bits; many of the resulting outages will be corrected by the outer Reed-Solomon code. At the same time, the mean time between false alarms is on the order of several years, independent of the signal-to-noise ratio.

Recently discovered procedures use a random input, rather than a cryptographic key, to turn a piece s of information into n + 1 pieces of information in such a way that s can be recovered from any b + 1 of them but that it is hard, or perhaps impossible in a sense which must be precisely defined, to recover s from any b of them. Thus, for example, one might have 15 pieces of information such that any 9 of them suffice to reconstitute s, but euch that no 8 of them give any hint as to what s is. The various authors of euch procedures have called them key safeguarding schemes, threshold schemes, secret sharing, and key sharing. None of these names captures the idea, which we will denote by information protection system (IPS). Our purpose is to put a rigorous foundation under the intuitive security arguments these papers adduce. In the proceed we will produce a distinctive style of proof of security, a rigorous argument involving product measures as a conceptual basis for justifying intuitively plausible probabilistic statement of the sort C. E. Shannon used to describe the security of the one-time pad.