Higher-Order Staircase Codes: A Unified Generalization of High-Throughput Coding Techniques
Abstract
We introduce a unified generalization of several well-established high-throughput coding techniques including staircase codes, tiled diagonal zipper codes, continuously interleaved codes, open forward error correction (OFEC) codes, and Robinson-Bernstein convolutional codes as special cases. This generalization which we term "higher-order staircase codes" arises from the marriage of two distinct combinatorial objects: difference triangle sets and finite-geometric nets, which have typically been applied separately to code design. We illustrate one possible realization of these codes, obtaining powerful, high-rate, low-error-floor, and low-complexity coding schemes based on simple iterative syndrome-domain decoding of coupled Hamming component codes. We study some properties of difference triangle sets having minimum scope and sum-of-lengths, which correspond to memory-optimal higher-order staircase codes.
Cite
@article{arxiv.2410.16504,
title = {Higher-Order Staircase Codes: A Unified Generalization of High-Throughput Coding Techniques},
author = {Mohannad Shehadeh and Frank R. Kschischang},
journal= {arXiv preprint arXiv:2410.16504},
year = {2025}
}
Comments
Submitted to 2025 IEEE International Symposium on Information Theory (ISIT 2025). arXiv admin note: text overlap with arXiv:2312.13415