On the Dynamics of Analog Min-Sum Iterative Decoders, an Analytical Approach

In this paper, we show that an ideal analog min-sum decoder, in the log-likelihood ratio domain, can be considered as a piecewise linear system. Many theoretical aspects of these decoders, thus, can be studied analytically. It is also shown that the dynamic equations can become singular and degrade the decoding performance. When the decoder is nonsingular, the corresponding dynamic equations can be solved analytically to derive outputs of the decoder. The proposed approach paves the way for further analytical analysis on the dynamics of analog min-sum decoders.