Higher-Order Staircase Codes: A Unified Generalization of High-Throughput Coding Techniques

TL;DR

This paper introduces higher-order staircase codes, a unified framework that generalizes multiple high-throughput coding techniques by combining difference triangle sets and finite-geometric nets, leading to efficient, high-rate, low-error coding schemes.

Contribution

It presents a novel unification of existing high-throughput codes through a new mathematical framework using difference triangle sets and finite-geometric nets.

Findings

Achieves high-rate, low-error-floor coding schemes

Provides simple iterative syndrome-domain decoding methods

Unifies multiple existing 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.