Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates
We analyze a class of high performance, low decoding data-flow codes suitable for high bit-rate optical-fiber communication systems. A spatially-coupled split-component ensemble is defined, encompassing the most representative codes in this class, staircase codes and braided block codes. Our definition preserves two important properties of this class of codes: deterministic partitioning of component-code bits over code blocks and simple iterative algebraic component-code decoding. For the binary erasure channel, we derive a vector recursion for the decoding process and determine its threshold using potential function analysis. We generalize the analysis to mixture ensembles consisting of more than one type of component code. The analysis extends to the binary symmetric channel by assuming mis-correction-free component-code decoding. An intuitive upper-bound on the number of errors correctable by the ensemble is derived. Finally, we analyze the threshold of spatially-coupled split-component ensembles under beyond bounded-distance component decoding.