Spatially Coupled Split-Component Codes With Iterative Algebraic Decoding

Abstract

We analyze a class of high performance, low decoding-data-flow error-correcting codes suitable for high bit-rate optical-fiber communication systems. A spatially coupled split-component ensemble is defined, generalizing from the most important codes of this class, staircase codes and braided block codes, and preserving a deterministic partitioning of component-code bits over code blocks. Our analysis focuses on low-complexity iterative algebraic decoding, which, for the binary erasure channel, is equivalent to a generalization of the peeling decoder. Using the differential equation method, we derive a vector recursion that tracks the expected residual graph evolution throughout the decoding process. The threshold of the recursion, for asymptotically long component codes, is found using potential function analysis. We generalize the analysis to mixture ensembles consisting of more than one type of component code. We give an example of a mixture ensemble consisting of two component codes, which has better performance than spatially-coupled split-component ensembles consisting of only one component code. The analysis extends to the binary symmetric channel by assuming miscorrection-free component-code decoding. Simple upper bounds on the number of errors correctable by the ensemble are derived. Finally, we analyze the threshold of spatially coupled split-component ensembles under beyond bounded-distance component decoding.