Performance evaluation of faulty iterative decoders using absorbing Markov chains

We propose an iterative decoder made of a combination of faulty and perfect logic gates that is capable of correcting more channel errors than its counterpart made completely of perfect logic gates. We present an error probability analysis based on absorbing Markov chains, and explain how the randomness in the check node update function helps a decoder to escape to local minima associated with trapping sets. For the (155, 64) Tanner low-density parity check code, we provide a range of gate failure probabilities for which imperfect decoders perform better.