Analysis of high order recurrent neural networks for analog decoding

Forward error correction coding (FEC) is a classical and well known technique to improve the efficiency of a digital transmission. Despite of intensive research in this field the Shannon limit was unachievable for a long time, but today iterative techniques can approach this limit. However, iterative decoding is computationally very demanding, especially for real time applications and/or high data rates. This encouraged researchers to look for alternatives, which led to the new field of analog decoding, meaning an implementation with analog circuits. The performance gain of those analog decoders compared to a digital implementation is believed to be at least a factor of 100 in terms of speed or power consumption. In this paper we focus on iterative threshold decoding. We show that this method can be considered as a dynamical system, which can be described by high order recurrent neural networks. Using this representation we give a qualitative description of the long term behavior of such a dynamical system. The continuous time high order recurrent neural networks can be understood as the basis for an analog implementation of iterative threshold decoding.