Generalized Stopping Sets and Stopping Redundancy

Iterative decoding for linear block codes over erasure channels may be much simpler than optimal decoding but its performance is usually not as good. Here, we present a general iterative decoding technique that gives a more refined trade-off between complexity and performance. In each iteration, a system of equations is solved. In case the maximum number of equations to be solved is just one, the general iterative decoder reduces to the well-known iterative decoder. On the other hand, if the maximum number is set to the redundancy of the codes, the general iterative decoder gives the same performance as the optimal decoder. Varying the maximum number of equations to be solved in each iteration between these two extremes allows for a better match, in terms of performance and complexity, to the system specifications. Stopping sets and stopping redundancy are important concepts in the analysis of the performance and complexity of iterative decoders on the erasure channel. In consequence of the new generalized decoding procedure, the notions of stopping sets and stopping redundancy are generalized as well. Basic properties and examples of both generalized stopping sets and generalized stopping redundancy are presented in this paper.