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A new decoding algorithm for burst-error-correction is proposed. The proposed algorithm can effectively correct burst errors of length approaching n - k symbols for (n, k) Reed-Solomon (RS) codes. Compared with existing algorithms, the algorithm enables much faster decoding with far less computational complexity.
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Introduction: Reed-Solomon (RS) codes have been proven to be very effective in correcting burst errors, whereas conventional decoding algorithms often assume that the occurrence of a symbol error is independent of that of others, and burst errors are treated as the same as random errors in the decoding procedure. According to the Singleton bound, the maximum length of burst errors that can be corrected by a (n, k) RS code is (n - k)/2. Recent studies have shown that, when error location correlation within a burst is properly employed, a burst error of length approaching n - k symbols may be effectively corrected with relatively small probabilities of miscorrection [1, 2]. In particular, one such bursterror-correcting algorithm was first presented by Chen and Owsely [1], and then modified by Dawson and Khodkar [3]. However, this decoding algorithm, as well as its modified version, is too complex for implementation and is likely to result in a long decoding delay. In this Letter, a new burst-error-correcting algorithm is proposed. It is shown that, compared with existing algorithms, the proposed algorithm enables much faster decoding with far less computational complexity.
Proposed algorithm: Assume that the error pattern of a burst is as follows:
... (1)
where v is the length of the burst, er is the error value of the rth erroneous symbol in the burst (where...