Serial List Viterbi Decoding with CRC: Managing Errors, Erasures, and Complexity
Serial List Viterbi Decoding with CRC: Managing Errors, Erasures, and Complexity
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使用 CRC 的串行列表维特比解码：管理错误、擦除和复杂性
DOI：
10.1109/glocom.2018.8647589
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
R. Wesel
中科院分区：
文献类型：
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作者：
Hengjie Yang;S. V. S. Ranganathan;R. Wesel
本文分析了与最佳的CRC代码结合使用的串行列表Viterbi算法（S-LVA），这些算法通过最大程度地减少未检测到的误差的可能性，从而最大程度地提高了通过CRC检查的卷积代码字之间的最小距离。特别是，本文确定了3GPP标准卷积代码的最佳CRC代码（561,753）。随着SNR的变化，最大列表大小范围从一个到最大值，本文使用界限，近似值和仿真来表征解码复杂性以及擦除概率和未检测到的错误概率之间的权衡。 S-LVA的复杂性是由检查通过CRC检查或L代码字所需的解码尝试数的预期值来捕获的。对于具有学位 - M CRC和最大可能L的S-LVA，这是所有可能的卷积代码字集的基础性，随着SNR的增加，解码尝试数量的预期值会收敛到一个，而2^m（1 -shr降低时，对于小ε> 0。对于最大可能L的S-LVA，擦除概率为零。随着l从最大值降低，擦除概率增加，UE概率降低到L = 1的概率，为此，UE概率被最近的邻居结合了。
This paper analyzes the serial list Viterbi algorithm (S-LVA) used in conjunction with optimal CRC codes that minimize probability of undetected error by maximizing the minimum distance between convolutional codewords that pass the CRC check, following Lou et al. In particular, the paper identifies such optimal CRC codes for the 3GPP standard convolutional code (561,753). As SNR varies and the maximum list size L ranges from one to its maximum, this paper uses bounds, approximations, and simulation to characterize decoding complexity and the trade-off between erasure probability and undetected error probability. The complexity of S-LVA is captured by the expected value of the number of decoding attempts required before a CRC check passes or L codewords have been examined. For S-LVA with a degree-m CRC and maximum possible L, which is the cardinality of the set of all possible convolutional codewords, the expected value of the number of decoding attempts converges to one as SNR increases and to 2^m(1-ε), for a small ε > 0, as SNR decreases. For S-LVA with the maximum possible L, the erasure probability is zero. As the L decreases from this maximum, the erasure probability increases and the UE probability decreases to that of L=1, for which UE probability is well approximated by a nearest-neighbor bound.