Generalized Iterative Decoding for Linear Block Codes on the Binary Erasure Channel

The generalized iterative decoding concept offers attractive performance versus complexity trade-off opportunities in the spectrum between traditional iterative decoding and optimal decoding for linear block codes over the binary erasure channel. In each iteration, a system of equations is solved. The maximum number of equations to be solved in one iteration is called the order of the decoder. In case the order is just one, the generalized iterative decoder reduces to the traditional iterative decoder. On the other hand, if the order is set to the redundancy of the codes, the generalized iterative decoder gives the same performance as the optimal decoder. Varying the order between these two extremes allows for a better match to the system specifications. In this paper, we consider aspects regarding the implementation of generalized iterative decoding and we determine the minimum order (as a function of the girth) that can potentially lead to improvement over traditional iterative decoding.