Approaching maximum likelihood performance of LDPC codes by stochastic resonance in noisy iterative decoders

In the 1960s-70s, Taylor and Kuznetsov obtained a remarkable result that information can be reliably retrieved from a noisy channel even if a decoder is made of noisy components. The results of Vasic and Chilappagari presented at the ITA Workshop ten years ago have revived the interest in decoders made of noisy hardware and since then a number of improvements of the iterative decoders have been made to bring their performance closer to that of their perfect counterparts. However, a common mantra has been that noisy decoders cannot be better than their perfect counterparts. In this talk we report an unexpected phenomenon we have recently discovered - noise can actually improve the error correction process by reducing the probability of decoding error, in some cases by more that two orders of magnitude. This new form of stochastic resonance enables us to use logic gate errors to correct channel errors. This novelty recognizes that the decoder - essentially an iterative minimization of the Bethe free energy on the code graph - can get trapped in local minima, and random perturbations help the decoder to escape from these minima and converge to a correct code-word. In the spirit of Marcus Tullius Cicero's "Clavus clavo eicitur," ("one nail drives out another") they operate on the principle: Error errore eicitur" - "one error drives out another." Crucially, such useful random perturbations require neither additional hardware nor energy, as they are built into the low-powered, noisy hardware itself.