Further Studies of Soft Decision Error Detectors for the Gaussian Channel

This correspondence is an extension of the work in [1] and [2]. We present two new classes of error detectors which utilize symbol reliability information (i.e., soft decision error detectors). First, a simple class of selectively single error correcting error detectors is discussed where the syndrome information is used and where just one single reliability number is compared to a threshold value. These error detectors are simpler than those in [1] and [2], but less powerful. Second, a class of soft decision error detectors with low probability of undetected errors is considered. The reliability information is used to reduce the probability of undetected errors without increasing the repeat request probability (compared to the hard decision error detector). Exponential properties for large signal-to-noise ratios and bounds are calculated for both classes of error detectors. Computer simulations are also presented.