Scenario-Simplified Successive Cancellation Decoding of Polar Codes for Channel With Deletions
Scenario-Simplified Successive Cancellation Decoding of Polar Codes for Channel With Deletions
复制标题
具有删除的信道的极化码的场景简化连续消除解码
DOI：
10.1109/access.2019.2897114
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发表时间：
2019-01-01
期刊：
影响因子：
3.9
通讯作者：
Liu, Rongke
中科院分区：
文献类型：
--
作者：
Tian, Kuangda;Liu, Rongke
最近提出了删除信道下极化码的逐次相消译码算法和相应的极化定理。在该译码算法中，传统的逐次相消译码网格中的每个节点根据不同的删除模式被划分为许多不同的场景。场景的数量随着删除错误<inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula>的数量的平方而增加，这导致高解码复杂度。为了降低解码复杂度，本文提出了删除信道上极化码的场景简化连续抵消解码算法。在所提出的解码算法中，我们使用精确的上界和下界来识别解码网格中每个节点的可行场景，并避免计算不可能的场景。通过重新排列情景指数表，可以简化情景指数的计算操作。我们还调查了每个场景的联合权重。通过设置阈值<inline-formula><tex-math notation="LaTeX">$\tau $</tex-math></inline-formula>来修剪具有低联合权重概率的场景，可以进一步降低复杂度。对于长度<inline-formula><tex-math notation="LaTeX">$N=512$</tex-math></inline-formula>和<inline-formula><tex-math notation="LaTeX">$d = 10$</tex-math></inline-formula>的极化码，当<inline-formula><tex-math notation="LaTeX">$\tau = 10^{-5}$</tex-math></inline-formula>时，我们可以减少42.5%的存储场景和46.8%的计算场景，而性能损失可以忽略不计。
Successive cancellation-based decoding algorithm and corresponding polarization theorems for polar codes over channels with deletions have been proposed recently. In that decoding algorithm, each node in the conventional successive cancellation decoding trellis is divided into many different scenarios according to different deletion patterns. The number of scenarios increases with the square of the number of deletion errors <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> which results in high decoding complexity. In this paper, to reduce the decoding complexity, we propose the scenario-simplified successive cancellation decoding algorithm for the polar codes over the deletion channel. In the proposed decoding algorithm, we use exact upper and lower bounds to identify the feasible scenarios of each node in the decoding trellis and avoid calculating the impossible scenarios. And by rearranging the scenario index table, the operations of calculating indices of scenarios can be simplified. We also investigate the joint-weight for each scenario. By setting a threshold <inline-formula> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> to prune the scenarios with low joint-weight probabilities, the complexity can be reduced further. For polar codes of length <inline-formula> <tex-math notation="LaTeX">$N=512$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$d = 10$ </tex-math></inline-formula>, we can reduce 42.5% stored scenarios and 46.8% computed scenarios when <inline-formula> <tex-math notation="LaTeX">$\tau = 10^{-5}$ </tex-math></inline-formula> with a negligible performance loss.