Generalized Piggybacking Codes for Distributed Storage Systems

Abstract

This paper generalizes the piggybacking constructions for distributed storage systems by considering various protected instances and piggybacked instances. Analysis demonstrates that the proportion of protected instances determines the average repair bandwidth for a systematic node. By optimizing the proportion of protected instances, the repair ratio of generalized piggybacking codes approaches zero instead of 50% as the number of parity check nodes tends to infinity. Furthermore, the computational complexity for repairing a single systematic node cost by generalized piggybacking codes is less than that of the existing piggybacking designs.

Distributed Storage Codes Based on Double- Layered Piggybacking Framework

“…Since the invention of piggybacking codes, researchers are trying to find effective piggybacking construction method to repair the failed nodes. In [27], S. Yuan et al introduced generalized piggybacking codes to repair the systematic nodes and proved that the average repair bandwidth ratio of systematic nodes can approach to zero with the number of parity nodes tending to infinity, which is very close to the cutset bound of distributed storage codes. In [28], S. Kumar et al also investigated a piggybacking framework for repairing systematic nodes, which is based on two classes of parity nodes.…”

“…To ensure that each systematic node can be recovered successfully, the data symbols in a systematic node cannot be embedded in the same piggyback block. Therefore, the data symbols need to be dispersed as much as possible [27]. According to the analysis, when the number of piggyback blocks is a constant, the number of data symbols embedded in every piggyback block directly affects the repair bandwidth of systematic nodes.…”

“…According to the analysis, when the number of piggyback blocks is a constant, the number of data symbols embedded in every piggyback block directly affects the repair bandwidth of systematic nodes. So, we choose the best solution and adopt the general idea [24], [27], [29], [37]. In our example, the embedding method is explained as follows.…”

Code Constructions for Distributed Storage With Low Repair Bandwidth and Low Repair Complexity

“…In this section, we compare the performance of the proposed codes with that of several codes in the literature, namely MDS codes, exact-repairable MDS codes [24], MDR codes [9], Zigzag codes [10], Piggyback codes [19], generalized Piggyback codes [23], EVENODD codes [25], Pyramid codes [2], and LRCs [3]. Throughout this section, we compare the repair bandwidth and the repair complexity of the systematic nodes with respect to other codes, except for exact-repairable MDS and BASIC PM-MBR codes.…”

“…The aforementioned notation, unlike our notation in this paper, refers to an (n, k, n − k) code that has λ ≤ 2 n−1 n−k , β = n − k, and repair locality of n − 1. For generalized Piggyback codes [23], we choose β = k. Also note that the parameters s, p are chosen according to [23,Eq. 20], i.e., s = k and p = k − s, whichever pair of values gives the lowest repair bandwidth.…”