This article corrects a minor error in a venerable contribution by Stein (1966) to the statistical theory of communication. The author shows that at high SNR, with optimum decision threshold, mark and space errors contribute equally to the average error probability.>

It is well known that on-off keying (OOK), i.e. the transmission of a pulse for a data one (mark) and transmission of no signal for a data zero (space), exhibits a 3 dB inferiority to antipodal signalling, in terms of the signal-to-noise ratio required to achieve a specified bit error probability. When the channel is characterized by the cutoff rate R/sub 0/, this 3 dB inferiority persists, in the sense that the required E/sub b//N/sub 0/ to operate at a given value of R/sub 0/ is 3 dB greater for the OOK channel than for the antipodal channel. However, it is shown that, if the definition of cutoff rate is generalized in an appropriate way to reflect the fact that signal energy is expended only in the transmission of marks, part of this penalty is recovered. In fact, it is shown that, in the limit of low R/sub 0/, there is no penalty in signal-to-noise ratio. Even at rates of realistic interest, the penalty is significantly less than the expected 3 dB.>

In this paper, we evaluate the performance of noninterleaved convolutional codes in the presence of Gaussian noise and periodic erasure bursts, with maximum likelihood (Viterbi) decoding. The results show that even for burst lengths that are a significant fraction of the code constraint length, the performance degradation is surprisingly small. It is then shown that in many of these cases the use of interleaving would provide very little performance gain. In addition, for burst lengths that are so long that interleaving is unavoidable, these results demonstrate the robustness of fixed periodic interleavers against variability in the parameters of the burst process.

The structure of punctured convolutional cedes is described, and it is indicated how their use simplifies the design of maximum likelihood decoders. The best codes of this class for rates 2/3 and 3/4 are tabulated and performance curves are given for these codes.

Power spectra for binary phase-shift keyed (PSK) and frequency-shift keyed (FSK) signals with combined sinusoidal amplitude modulation by the bit rate clock are presented. Such signal formats have application in "burst" communication systems wherein reliable bit synchronization is provided with relative receiver simplicity. Effects of the clock amplitude modulation index and phase are considered, and corresponding power spectra are illustrated. Further, effects of the clock parameters on the rate of spectral rolloff are given and compared with those of conventional PSK and FSK spectra.

This paper investigates some of the properties of a class of two-level codes with constrained run length, whose use has been proposed for purposes of bandwidth compression. It is shown that such codes can indeed reduce the bandwidth containing a given percentage of the transmitted power. To communicate information, however, different transmitted codewords must be distinguishable at the receiver, and this requires that the channel bandwidth be sufficiently wide to allow the difference waveform to propagate. It is demonstrated that decreasing theX-percent bandwidth using these codes leads to a rapid increase in the difference waveform bandwidth, and hence in the channel bandwidth necessary to maintain error rate performance. Thus, these codes are bandwidth expansion codes in disguise. Signal-to-noise ratio and channel bandwidth requirements for these codes are discussed and compared with those ofM-level codes [pulse-amplitude modulation (PAM)] for two kinds of receivers.

Sequential decoding procedures are studied in the context of selecting a path through a tree. Several algorithms are considered and their properties compared. It is shown that the stack algorithm introduced by Zigangirov and by Jelinek is essentially equivalent to the Fano algorithm with regard to the set of nodes examined and the path selected, although the description, implementation, and action of the two algorithms are quite different. A modified Fano algorithm is introduced, in which the quantizing parameter\Deltais eliminated. It can be inferred from limited simulation results that, at least in some applications, the new algorithm is computationally inferior to the old; however, it is of some theoretical interest since the conventional Fano algorithm may be considered to be a quantized version of it.