Layered, Exact-Repair Regenerating Codes Via Embedded Error Correction and Block Designs

TL;DR

This paper introduces a new class of exact-repair regenerating codes constructed via embedded error correction and block designs, achieving better performance than traditional space-sharing methods and approaching optimal tradeoffs.

Contribution

The paper presents a novel code construction method that combines erasure correction codes with block design stitching, enabling low-complexity decoding and improved performance.

Findings

Achieves better performance than space-sharing between MSR and MBR codes.

First codes to reach this performance level on the functional-repair tradeoff.

Asymptotically optimal at high rates, approaching minimal storage and repair bandwidth.

Abstract

A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the "help-by-transfer" property where the helper nodes simply transfer part of the stored data directly, without performing any computation. This embedded error correction structure makes the decoding process straightforward, and in some cases the complexity is very low. We show that this construction is able to achieve performance better than space-sharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes, and it is the first class of codes to achieve this performance. In fact, it is shown that the proposed construction can achieve a non-trivial point on the optimal functional-repair tradeoff, and it is asymptotically optimal at high rate, i.e., it asymptotically approaches the minimum storage and the minimum repair-bandwidth simultaneously.