Efficiently Decodable Low-Rate Codes Meeting Gilbert-Varshamov Bound
نویسندگان
چکیده
We demonstrate a probabilistic construction of binary linear codes meeting the GilbertVarshamov bound (with overwhelming probability) for rates up to about 10−4, together with polynomial time algorithms to perform encoding and decoding up to half the distance. This is the first such result (for some positive rate) with polynomial decoding complexity; previously a similar result (up to rate about 0.02) was known with sub-exponential time decoding (Zyablov and Pinsker, 1981).
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