Decoding real-number convolutional codes: change detection, Kalman estimation

Abstract

Convolutional codes which employ real-number symbols are difficult to decode because of the size of the alphabet and the numerical and roundoff noise inherent in arithmetic operations. Such codes find applications in both channel coding for communication systems and in fault-tolerance support for signal processing subsystems. A new method for error correction based on optimum mean-square recursive Kalman estimation techniques incorporates time-varying models for the system and associated disruptive noise sources. The underlying common model for communications and fault tolerance applications assumes the system operates nominally with low levels of channel or numerical and roundoff noise, occasionally experiencing temporarily larger noise statistics. A time-varying Kalman estimation structure which uses single-step and fixed-lag smoothing predictors can correct errors to within the nominal low-noise levels. Correction actions may be activated only when larger activity is detected, so methods for detecting possible error situations are developed. However, misdetection is not a serious problem because the Kalman correction methods only track significant errors in the data. Two activity detection techniques are examined; one is based on likelihood ratio tests while another uses clipped samples and binary pattern matching. Several examples showing simulated mean-square error performance and decoded waveforms from error injection experiments are presented.