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

2024-10-21

arXiv.org

AI Summary

To address the urgent demand for high-throughput, low-error-floor, low-latency, and memory-efficient coding in high-speed optical communication and storage systems, this paper proposes a unified high-order staircase code framework. Our method is the first to synergistically integrate two combinatorial structures—differential triangular sets and finite geometry nets—to construct coupled Hamming component codes, enabling iterative check-domain decoding. We theoretically prove that the framework achieves information-theoretically optimal memory consumption. Experiments demonstrate substantial reductions in error floor and decoding latency while maintaining high code rates and low decoding complexity. Beyond unifying and generalizing existing high-throughput paradigms—including conventional staircase codes and tile-diagonal zipper codes—our work establishes a novel combinatorial-design-driven coding construction paradigm. This provides both a practically viable theoretical foundation and architectural support for next-generation high-speed data transmission and storage systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Combinatorial Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Coding Techniques
• Information Processing
• Error Reduction

Innovation

• High-order Staircase Codes
• Differential Triangle Sets
• Finite Geometric Lattices