This paper examines more closely the probabilistic dynamics of queueing timing channels and discusses a new practical coding scheme which is tailored to them and approaches capacity. We consider using sparse graph coset codes over non-binary finite fields. We use a shaping technique to map algebraic symbols to non-uniform codewords using the inverse cumulative distribution of a target random variable. We exploit the graphical structure of the conditional distribution of the departure process given the arrival process to arrive at a Forney Factor graph of the joint likelihood that has graphical structure reminiscent of coding on inter-symbol interference channels with LDPC codes. We show through simulation that this technique, when using low-complexity iterative decoding, is capacity-approaching.
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