The Minimum Distance of Turbo-Like Codes
The Minimum Distance of Turbo-Like Codes
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类 Turbo 码的最小距离
DOI：
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发表时间：
2009
影响因子：
2.5
通讯作者：
D. Spielman
中科院分区：
文献类型：
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作者：
L. Bazzi;Mohammad Mahdian;D. Spielman
给出了并行级联Turbo码、串行级联卷积码、重复累加码、重复卷积码的最小距离的最坏情况上界，以及通过允许非线性和大存储组成码而得到的这些码的推广。结果表明，具有次线性记忆的并行级联Turbo码和重复卷积码是渐近不好的。还证明了具有恒定记忆外码和次线性记忆内码的深度二串行级联码是渐近不好的。即使当卷积编码器被一般的有限状态自动机编码器取代时，这些上界中的大多数仍然有效。相反，证明了通过随机排列将一个重复码与两个累加器码级联而得到的深度三串行级联码是渐近好的。
Worst-case upper bounds are derived on the minimum distance of parallel concatenated turbo codes, serially concatenated convolutional codes, repeat-accumulate codes, repeat-convolute codes, and generalizations of these codes obtained by allowing nonlinear and large-memory constituent codes. It is shown that parallel-concatenated turbo codes and repeat-convolute codes with sub-linear memory are asymptotically bad. It is also shown that depth-two serially concatenated codes with constant-memory outer codes and sublinear-memory inner codes are asymptotically bad. Most of these upper bounds hold even when the convolutional encoders are replaced by general finite-state automata encoders. In contrast, it is proven that depth-three serially concatenated codes obtained by concatenating a repetition code with two accumulator codes through random permutations can be asymptotically good.