The Theory Behind Perturbed Decoding Algorithm

In perturbed decoding algorithm (PA), independently perturbed versions of the originally received signal are passed through a decoder in order to obtain several distinct decoder outputs. PA can be used to enhance the performance of a concatenated coded system, especially for those where multiple-output inner decoder is unavailable. A number of questions regarding PA remain unanswered, including how best the original signal is to be perturbed, the distribution of the number of perturbed decodings, and the compatibility of PA with various kinds of error control codes. In this paper, we derive the distribution of the number of perturbed decoding given independent Gaussian perturbations. The dominant terms of the distribution indicate that the complexity of PA is highly dependent on the geometric structure of the error control code. Subsequently, for ML inner decoder, we derive the optimal signal-to-perturbation noise level given the operating SNR and the two-centroid spectrum of the inner code. Computer simulation is conducted. The results are consistent with our analysis.