Higher-Order Staircase Codes

TL;DR

This paper introduces higher-order staircase codes that leverage difference triangle sets and finite-geometric nets to achieve high-rate, low-error, and low-complexity coding schemes suitable for high-throughput communication systems.

Contribution

It generalizes staircase and zipper codes by allowing each symbol to be protected by multiple component codes, combining combinatorial objects for improved code design.

Findings

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

Enables memory-optimal realizations of higher-order staircase codes

Potential to improve performance-complexity-latency tradeoffs in fiber-optic communications

Abstract

We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. 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 demonstrate 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 anticipate that the proposed codes could improve performance--complexity--latency tradeoffs in high-throughput communications applications, most notably fiber-optic, in which classical staircase codes and zipper codes have been applied. We consider the construction of difference triangle sets having minimum scope and sum-of-lengths, which lead to memory-optimal realizations of higher-order staircase codes. These results also enable memory reductions for early families of convolutional codes constructed from difference triangle sets.