Showing papers by "Codex Corporation published in 1970"
TL;DR: Minimal encoders are shown to be immune to catastrophic error propagation and, in fact, to lead in a certain sense to the shortest decoded error sequences possible per error event.
Abstract: A convolutional encoder is defined as any constant linear sequential circuit. The associated code is the set of all output sequences resulting from any set of input sequences beginning at any time. Encoders are called equivalent if they generate the same code. The invariant factor theorem is used to determine when a convolutional encoder has a feedback-free inverse, and the minimum delay of any inverse. All encoders are shown to be equivalent to minimal encoders, which are feedback-free encoders with feedback-free delay-free inverses, and which can be realized in the conventional manner with as few memory elements as any equivalent encoder, Minimal encoders are shown to be immune to catastrophic error propagation and, in fact, to lead in a certain sense to the shortest decoded error sequences possible per error event. In two appendices, we introduce dual codes and syndromes, and show that a minimal encoder for a dual code has exactly the complexity of the original encoder; we show that systematic encoders with feedback form a canonical class, and compare this class to the minimal class.
801 citations
TL;DR: It turns out that a simple encoder in combination with a decoder of modest complexity placed into an uncoded communications system can increase the data rate by a factor of four or more depending on the coding scheme and the allowable error rate.
Abstract: Between 1948?when Shannon first proposed his basic theorems on information theory?and the start of the space age, little practical application developed from the lessons of coding theory. This article presents an overview of the Shannon theorem, interesting practical codes, and their application to the space channel. It turns out that a simple encoder in combination with a decoder of modest complexity placed into an uncoded communications system can increase the data rate by a factor of four or more depending on the coding scheme and the allowable error rate. Use of a convolutional code with sequential decoding has proved to be the outstanding scheme for these applications. It appears that, in the future, coding will find a place in most new digital space communication systems.
42 citations