Fast transform decoding of nonsystematic Reed-Solomon codes

A Reed-Solomon (RS) code is considered to be a special case of a redundant residue polynomial (RRP) code, and a fast transform decoding algorithm to correct both errors and erasures is presented. This decoding scheme is an improvement of the decoding algorithm for the RRP code suggested by Shiozaki and Nishida, and can be realized readily on very large scale integration chips

Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs

A novel technique, based on the pseudo-random properties of certain graphs known as expanders, is used to obtain novel simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling, and then regrouping the code coordinates. For any fixed (small) rate, and for a sufficiently large alphabet, the codes thus obtained lie above the Zyablov bound. Using these codes as outer codes in a concatenated scheme, a second asymptotic good construction is obtained which applies to small alphabets (say, GF(2)) as well. Although these concatenated codes lie below the Zyablov bound, they are still superior to previously known explicit constructions in the zero-rate neighborhood

Augmented burst-error correction for UNICON laser memory

A single-burst-error correction system is described for data stored in the UNICON laser memory. In the proposed system, a long fire code with code length n greater than 16,768 bits was used as an outer code to augment an existing inner shorter fire code for burst error corrections. The inner fire code is a (80,64) code shortened from the (630,614) code, and it is used to correct a single-burst-error on a per-word basis with burst length b less than or equal to 6. The outer code, with b less than or equal to 12, would be used to correct a single-burst-error on a per-page basis, where a page consists of 512 32-bit words. In the proposed system, the encoding and error detection processes are implemented by hardware. A minicomputer, currently used as a UNICON memory management processor, is used on a time-demanding basis for error correction. Based upon existing error statistics, this combination of an inner code and an outer code would enable the UNICON system to obtain a very low error rate in spite of flaws affecting the recorded data