Unconventional behavior of the noisy min-sum decoder over the binary symmetric channel

This paper investigates the behavior of the noisy Min-Sum decoder over binary symmetric channels. A noisy decoder is a decoder running on a noisy device, which may introduce errors during the decoding process. We show that in some particular cases, the noise introduce by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length, by using “noisy” density evolution equations, and it is also verified in the finite-length case by Monte-Carlo simulation.