Analog Codes for Gross Error Correction in Signal Transmission

We proposed a novel decoding algorithm for Analog Codes (Reed-Solomon Codes over complex numbers), the syndrome repairing (SR) algorithm, for gross error correction in signal transmission. Simulations show that, if the number of gross errors is not too large and the amplitude of background noise is small enough (compared to the amplitude of gross errors), the SR algorithm recovers the original signal with nearly the same accuracy as if no gross errors occur upon transmission. In particular, if the transmission is background-noise-free, then the recovery is exact. Introduction Analog Codes, or DFT Codes [1] is a class of Reed-Solomon Codes over the complex field which allows for the detection and correction of multiple errors. The applications of Analog Codes for multiple errors correction in the transmission of continuous-amplitude signals has been discussed by many authors [2,3]; and can be summarized as follows. Assume we wish to send a signal to a remote receiver via a channel composed of background noise (or simply, noise) plus gross errors (or simply, errors) reliably. --Here we distinguish noise and errors by their amplitudes. More concretely, by noise we mean a random vector with each of its entries having Gaussian distribution m u