This paper discusses the theory and design of a tactical channel simulator (TCS) built to simulate land-mobile VHF radio links. The instrument is one of the first such units based on the stored channel principle, which permits the actual medium to be recorded and played back. The key application of the TCS simulator is to realistically reproduce field conditions in a laboratory. Tests on the TCS simulator should be in good accord with performance encountered in the field, unlike results obtained in the standard back-to-back tests which ignore effects of the propagation channel. Experimental results show that the evaluation of modem performance must take into account the effects of propagation over the VHF channel, as data tests are measurably affected by channel conditions. The TCS simulator will be particularly useful in the comparative evaluation of various highspeed, high-performance modems now being introduced into the inventory.

Through a careful examination of the equations by which Wald determines the values of the boundaries for tests of sequential hypotheses, we are able to obtain interesting relationships for the conditional probability distributions of the stage at which the test terminates. These enable us to study sequential tests in which the boundaries are functions of the sample number. We are particularly concerned with tests with convergent boundaries, and investigate a set of boundaries which approach those of a truncated Wald test. Approximate expressions for the expected sample number and probabilities of error are obtained for the tests considered. The obtained approximations apply best for gently tapering slopes. Extensions of our method can be applied to evaluate various ad hoc schemes for truncating tests and to the theory of tests with a varying parameter.

This paper formalizes the discussion of some structural properties of the generators for binary convolutional codes. The use of these properties may be helpful in the selection of generators which produce codes with desired error-correcting properties for sequential decoding. The approach taken is to decompose a generator sequence into subsequences called "subgenerators." The set of all such possible subsequences starting with a1is shown to form an Abelian group with respect to a binary convolution. The recurrence relation which permits the construction of the inverse of an encoding subgenerator is given. One application of these results is a simple proof of the reproducing property of the truncated convolutional message set noted by Wozencraft and Reiffen. The notion of "adjoint" canonical generators, all of which have the same error-correcting properties but different message sets, is also introduced. The distinction between encoding and decoding constraint lengths is pointed out and an estimate made of the achievable difference between the two. An efficient search procedure to select the generator of rate1/2which possesses the best error-correcting properties is also discussed. Selected generators of rates1/2and1/3are tabulated up to(32, 16)and(21, 7), respectively.

A device which performs a sequential test on a mixture of signal and noise is called a Sequential Detector. With such a device, two thresholds are introduced, each of which is associated with a terminal decision. The length of the detection process (integration time) is not fixed in advance of the experiment but is a random variable, depending on the progress of the test. An optimum form of such a test exists and is characterized by the fact that detection is performed on the average faster than with conventional; i.e., fixed sample size (optimum or non-optimum), devices. The sequential analysis developed by A. Wald is fully applied in this paper, but an important new feature is the treatment of correlated samples and its application to continuous sampling processes. In the introduction, the problem is presented within the framework of Wald's Statistical Decision Theory, and the optimum properties of sequential detectors are discussed accordingly. It is pointed out that a sequential detector is defined in terms of conditional probabilities and hence its operation is essentially independent of a priori information, although the average risk or cost of detection necessarily depends on the a priori signal data. The general theory is illustrated with some cases of special interest. The simplest example of detection involves independent, discrete observations; e.g., the case of a pulsed carrier in normal noise. Here the optimum detector still has the well-known\log I_0structure, but it is shown that the square law approximation for weak signals requires a bias correction due to the fourth order term. Coherent sequential detection of causal signals in normal noise provides another illustration of the theory. An interesting result is that the probabilities of error do not depend on the shape of the filter, provided the proper computer is used. The use of RC-filtered noise illustrates the treatment of continuous detection processes. Finally, the reduction in minimum detectable signal level resulting from the use of a sequential detector is computed. A third example is the sequential detection of random signals in normal noise. It is shown that, although the optimum computer involves the knowledge of the inverted correlation matrix, the average length of the test does not. Hence a curious result is obtained that in this instance detection can be performed in an arbitrarily short time. The paper concludes with a discussion of the practical necessity of truncating the detection process and exact expressions for the error probabilities of such truncated tests are derived and compared with Wald's original approximations.