Iterative decoding with flooding schedule can be formulated as a fixed-point problem solved iteratively by successive substitution (SS) method. la this work, we model continuous-time analog (asynchronous) iterative decoding by a first-order differential equation, and show that it can be approximated as the application of the well-known successive over relaxation (SOR) method for solving the fixed-point problem. Simulation results for belief propagation (sum-product) and min-sum algorithms confirm that SOR, which is in general superior to the simpler SS method, can considerably improve the performance of iterative decoding for short codes. The improvement in performance increases with the maximum number of iterations and by reducing the step size in SOR, and the asymptotic result, corresponding to infinite maximum number of iterations and infinitesimal step size represents the performance of continuous-time analog iterative decoding. This means that under ideal circumstances continuous-time analog decoders can outperform their discrete-time digital counterparts by a large margin. Moreover, the results obtained by the proposed model are surprisingly close to the results of circuit simulation of a min-sum analog decoder presented in [1]. Our work also suggests a general framework for improving iterative decoding algorithms on graphs with cycles, even for synchronous digital implementations.

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Conference Proceedings - 2004 IEEE International Symposium on Information Theory
Citation
Hemati, S. (Saied), & Banihashemi, A. (2004). On the dynamics of continuous-time analog iterative decoding. In IEEE International Symposium on Information Theory - Proceedings.