Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon code, as described by Schmidt et al. If this decoder does not succeed, it may either fail to return a codeword or miscorrect to an incorrect codeword, and good upper bounds on the fraction of error matrices for which these events occur are known. The decoding algorithm immediately applies to interleaved alternant codes as well, i.e., the subfield subcodes of interleaved Reed-Solomon codes, but the fraction of decodable error matrices differs, since the error is now restricted to a subfield. In this paper, we present new general lower and upper bounds on the fraction of error matrices decodable by Schmidt et al.'s decoding algorithm, thereby making it the only decoding algorithm for interleaved alternant codes for which such bounds are known.
翻译:Reed-Solomon Interleft Reed-Solomon 代码允许有效的解码算法,这些算法纠正的破解错误远远超过随机错误制度中最低距离的一半,例如,按照Schmidt 等人的描述,计算出每个Reed-Solomon 代码关键方程式的共同解决方案。如果这个解码器不成功,它可能无法返回一个代码或错误错误到错误的代码字典,并且对发生这些事件的错误矩阵的分数有良好的上限。解码算法立即适用于间断的偏差代码,例如,间断的Reed-Solomon 代码的子字段子代码,但可破解错误矩阵的分数有所不同,因为错误现在局限于一个子字段。在本文件中,我们对可被Schmidt 等人解码的错误矩阵的分数提出了新的一般下限和上下限,从而它成为已知这些界限的唯一解码。