Efficient Burst Error Correction by Hermitian Codes
نویسندگان
چکیده
Hermitian codes belong to a powerful class of algebraic geometry codes, which allow to correct many independent errors. We show that Hermitian codes can correct many bursts of errors as well. Decoding of a Hermitian (N,K) code over q2 can be reduced to decoding of interleaved extended Reed-Solomon codes. Using this fact, we propose an efficient unique decoding algorithm correcting up to (N −K)/(q + 1) phased bursts of length q. Decoding failure probability is upper bounded by 1/q and exponentially decreases with the number of bursts. It is also shown that low rate Hermitian codes can correct even more bursts of errors using “power” and “mixed” decoding. Time complexity of the algorithms is O(N) field operations.
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