Repairing Reed-Solomon Codes

Repairing Reed-Solomon Codes With Multiple Erasures

Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the whole file to be reconstructed in order to recover a single erased codeword symbol. In a recent work, Guruswami and Wootters (STOC’16) proposed a single-era...

Quantum Reed-Solomon Codes

During the last years it has been shown that computers taking advantage of quantum mechanical phenomena outperform currently used computers. The striking examples are integer factoring in polynomial time (see [8]) and finding pre– images of an n–ary Boolean function (“searching”) in time O( √ 2n) (see [5]). Quantum computers are not only of theoretical nature—there are several suggestions how t...

Parallel Reed-Solomon Codes

The compound and integrated parallel Reed-Solomon (RS) codes for multichannel communication systems are suggested. The matrix model of errors for such codes is investigated. Methods of coding and decoding of parallel RS codes, and also methods of increase of their error correcting capability are developed.

Reed-solomon Group Codes

Notes on Reed-solomon Codes

Reed-Solomon codes are examples of error correcting codes, in which redundant information is added to data so that it can be recovered reliably despite errors in transmission or storage and retrieval. The error correction system used on CD’s and DVD’s is based on a Reed-Solomon code. These codes are also used on satellite links and other communications systems. We will first discuss the general...