Quantizing for Correlation Decoding

Abstract

The increase in error rate due to quantizing is examined for the special case of a digital correlation decoder such as can be used for orthogonal and other block codes. Three types of effect are considered separately: 1) the increase in variance, which is proportional to the square of the quantum interval; 2) a threshold, proportional to the quantum interval, caused by the ambiguity when the received signal correlates equally with two code words; 3) the effect of limiting. Approximations are obtained for small quantizing loss, the case of greatest interest since the object of correlation decoding is high efficiency. For a 7-bit biorthogonal code and a total of 16 quantum levels the increase in error rate is computed as a function of the quantum interval, and an optimum is found.