Generalized Staircase Codes With Arbitrary Bit Degree
0Mohannad Shehadeh (University of Toronto)
https://simons.berkeley.edu/talks/mohannad-shehadeh-university-toronto-2024-03-06
Application-Driven Coding Theory
Staircase codes and their generalizations have proven to be a highly-competitive paradigm for high-rate, high-throughput, and high-reliability forward error correction, particularly in fiber-optic communications where such codes have been selected for various standardized transmission schemes. In this work, we propose a natural, non-trivial generalization of staircase codes in which each transmitted symbol is protected by an arbitrary number of component codewords rather than only two. Key ingredients of the construction are Golomb rulers (and their difference-triangle set generalizations) as well as an object from finite geometry called a (k,s)-net that forms a type of partial geometry. Allowing for a larger bit degree permits use of weak algebraic component codes such as extended Hamming codes, resulting in substantial reductions in decoding complexity and, we anticipate, decoder power consumption with only minor sacrifice in performance compared with staircase codes.