论文标题
平行性与潜伏期的简化连续分解极性代码
Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes
论文作者
论文摘要
本文描述了硬件资源约束下的极地代码的简化连续策略（SSC）解码方案的延迟。特别是，当可以同时执行SSC解码操作的处理元素$ p $与实践中的情况有限时，SSC解码的延迟为$ o \ left（n^{1-1/μ}+\ \ \\ frac {n} n} n} p} {p} {p} \ log_2 \ log_2 \ log_2 \ log_2 \ frac $ n $ n $ n $ n}代码和$μ$是通道的缩放指数。提出了该约束的三个直接后果。首先，在完全平行的实现中，其中$ p = \ frac {n} {2} $，ssc解码的延迟为$ o \ left（n^{1-1/μ} \ right）$，这是块长度的sublinear。这从我们的早期工作中恢复了结果。其次，在$ p = 1 $的完全串行实现中，SSC解码量表的延迟为$ o \ left（n \ log_2 \ log_2 n \ right）$。还计算了乘法常数：我们表明，当$ p = 1 $由$ \ left（2+o（1）\ right）n \ log_2 \ log_2 n $给出时，SSC解码的延迟在$ p = 1 $时。第三，在半平行的实现中，最小的$ p $具有与完全平行实现的延迟相同的延迟为$ p = n^{1/μ} $。通过广泛的模拟，我们对SSC解码潜伏期的紧密度和上述结果的适用性得到了验证。
This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints. In particular, when the number of processing elements $P$ that can perform SSC decoding operations in parallel is limited, as is the case in practice, the latency of SSC decoding is $O\left(N^{1-1/μ}+\frac{N}{P}\log_2\log_2\frac{N}{P}\right)$, where $N$ is the block length of the code and $μ$ is the scaling exponent of the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where $P=\frac{N}{2}$, the latency of SSC decoding is $O\left(N^{1-1/μ}\right)$, which is sublinear in the block length. This recovers a result from our earlier work. Second, in a fully-serial implementation where $P=1$, the latency of SSC decoding scales as $O\left(N\log_2\log_2 N\right)$. The multiplicative constant is also calculated: we show that the latency of SSC decoding when $P=1$ is given by $\left(2+o(1)\right) N\log_2\log_2 N$. Third, in a semi-parallel implementation, the smallest $P$ that gives the same latency as that of the fully-parallel implementation is $P=N^{1/μ}$. The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.
