Outer bounds for exact repair codes
Outer bounds for exact repair codes
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发表时间：
2014-06
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通讯作者：
I. Duursma
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作者：
I. Duursma
我们解决的开放性问题，建立率区域的精确修复再生码给定的参数（n，k，d）。Tian确定了（4，3，3）代码的速率区域，发现它严格位于功能修复速率区域内。使用不同的方法，Sathoor和Kumar证明了对于k>=3的码，函数修复外界和精确修复外界之间的非零间隙。我们的主要结果是两个改进的外界的确切修复再生码。他们捕捉，然后扩展的证明田和撒哈拉，森托尔和库马尔的重要部分。我们表明，边界可以结合进一步的改进。
We address the open problem of establishing the rate region for exact-repair regenerating codes for given parameters (n,k,d). Tian determined the rate region for a (4,3,3) code and found that it lies strictly within the functional-repair rate region. Using different methods, Sasidharan, Senthoor and Kumar proved a non-vanishing gap between the functional-repair outer bound and the exact-repair outer bound for codes with k>=3. Our main results are two improved outer bounds for exact-repair regenerating codes. They capture and then extend essential parts in the proofs by Tian and by Sasidharan, Senthoor and Kumar. We show that the bounds can be combined for further improvements.