# Message-round probability in SCCC graph

I am reading the paper Interleaver Design for Serial Concatenated Convolutional Codes by Yu et al., and it states the concept of message-round probability as $$F(l_1)F(l_2)$$ where $$F(l)$$ refers to the message-propagation function, which is a function decreasing with $$l$$ that gives the probability that a message propagates over more than $$l$$ symbols on an encoding branch; and $$l_1$$ is form the outer encoder while $$l_2$$ is from the inner encoder of a serially concatenated code. This way the message-round probability gives the probability that a message does a cycle of length $$l_1+l_2$$.

Such information is useful in order to design efficient interleavers to construct Turbo codes with lower error floors. The paper I cited above referes to two other papers in order to get a more concrete definition of $$F(l)$$ and ways to calculate such parameter, but they are not useful as one of the references is not available (it is a PhD disertation) and the other one gives no information about it (it is an older paper by the author). It would be very helpful is someone could give reference to some paper that deals with the issue or give some insight on it.

• I am not sure if this is the site where I should ask for this question, as I am not sure where the topcs related with coding theory should be posted. If anyone thinks that this should go in mathematics or computer science, please tell me and I will ask the question there. – Josu Etxezarreta Martinez Oct 8 '18 at 15:37