A geometric approach to incomplete soft decision block decoding

Two soft-decision incomplete decoding rules based on geometric considerations are proposed and analyzed for binary antipodal signaling on an additive white Gaussian channel. It is seen that for high signal to noise ratios, low decoder error probabilities are attainable requiring approximately 2 dB less power than equivalent hard-decision decoding schemes without a significant loss in performance due to rejections. The incomplete decoding rules allow the implementation of a new reduced complexity decoding algorithm based on a processing loop constructed around an encoder. Initial results indicate the performance of this new decoder compares favorably with that of the ideal decoder.<>