Bounds on separating redundancy
Bounds on separating redundancy
复制标题
分离冗余的界限
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
P. Vandendriessche
中科院分区：
文献类型：
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作者：
Y. Tsunoda;Yuichiro Fujiwara;Hana Ando;P. Vandendriessche
众所周知，任何线性码都允许在错误擦除信道上单独处理错误和擦除的解码策略。特别地，精心设计的奇偶校验矩阵使得通过迭代解码进行有效的擦除校正成为可能，同时立即提供必要的奇偶校验方程以用于按需独立纠错。给定线性码的分离冗余是具有该错误擦除分离所需属性的最小奇偶校验矩阵中的奇偶校验方程的数量。在某种意义上，它是线性代码的一个参数，表示有效地将擦除与错误分离的最小开销。虽然分离冗余的几个界限是已知的，但除了少数有限的情况外，在上限和下限之间仍然存在很大的差距。本文利用概率组合学和设计理论，改进了分离冗余度的上下界。
It is known that any linear code allows for a decoding strategy that treats errors and erasures separately over an error-erasure channel. In particular, a carefully designed parity-check matrix makes efficient erasure correction possible through iterative decoding while instantly providing the necessary parity-check equations for independent error correction on demand. The separating redundancy of a given linear code is the number of parity-check equations in a smallest parity-check matrix that has the required property for this error-erasure separation. In a sense, it is a parameter of a linear code that represents the minimum overhead for efficiently separating erasures from errors. While several bounds on separating redundancy are known, there still remains a wide gap between upper and lower bounds except for a few limited cases. In this paper, using probabilistic combinatorics and design theory, we improve both upper and lower bounds on separating redundancy.