Batch Codes Through Dense Graphs Without Short Cycles

• Published in: IEEE transactions on information theory Vol. 62; no. 4; pp. 1592 - 1604
• Main Authors: Rawat, Ankit Singh, Zhao Song, Dimakis, Alexandros G., Gal, Anna
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic methods; availability; Batch codes; Bipartite graph; Codes; codes with locality; coding for distributed storage; coding for parallel accesses; Context; Decoding; Fault tolerance; Fault tolerant systems; Graph algorithms; Information theory; Servers; Systematics; codes with locality; Batch codes; availability; coding for parallel accesses; coding for distributed storage
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2016.2524007

Consider a large database of n data items that need to be stored using m servers. We study how to encode information so that a large number k of read requests can be performed in parallel, while the rate remains constant (and ideally approaches one). This problem is equivalent to the design of multiset batch codes introduced by Ishai et al. We give the families of multiset batch codes with asymptotically optimal rates of the form 1-1/poly(k) and a number of servers m scaling polynomially in the number of read requests k. An advantage of our batch code constructions over most previously known multiset batch codes is explicit and deterministic decoding algorithms and asymptotically optimal fault tolerance. Our main technical innovation is a graphtheoretic method of designing multiset batch codes using dense bipartite graphs with no small cycles. We modify prior graph constructions of dense, high-girth graphs to obtain our batch code results. We achieve close-to-optimal tradeoffs between the parameters for bipartite graph-based batch codes.