An Efficient (n, k) Information Dispersal Algorithm for High Code Rate System over Fermat Fields

• Published in: IEEE communications letters Vol. 16; no. 12; pp. 2036 - 2039
• Main Authors: Lin, Sian-Jheng, Chung, Wei-Ho
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2012; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Coding, codes; Complexity theory; Decoding; Encoding; Erasure codes; Exact sciences and technology; fast Fourier transforms; information dispersal algorithm (IDA); Information, signal and communications theory; Polynomials; Reed-Solomon codes; Signal and communications theory; Systematics; Telecommunications and information theory; Reed Solomon code; Distributed memory; Reed-Solomon codes; fast Fourier transforms; Codec; Fast Fourier transformation; information dispersal algorithm (IDA); Telecommunication system; Storage system; Shadow; Erasure codes; Algorithm
• ISSN: 1089-7798
• DOI: 10.1109/LCOMM.2012.112012.121322

The (n, k) information dispersal algorithm (IDA) is the art of converting a file into n pieces of shadows, and any k out of the n shadows suffice for reconstructing the file. The IDA is applicable to the distributed communication and storage systems. This letter proposes an efficient (n, k) IDA for the case n/2≤k<;n over Fermat field GF(2 r +1). We first present the IDA under conditions of n-k in the power of 2 and n as multiple of n-k, and then extend the algorithm to the general case. For a reasonably large file, both encoder and decoder achieveΘ(nlog(n-k)) operations in processing k symbols.