极化码标度行为的泛界
Universal Bounds on the Scaling Behavior of Polar Codes
摘要：
我们考虑的问题，确定之间的权衡的速率和块长度的极化码对于一个给定的块错误概率时，我们使用的连续消除解码器。我们采取的Bhattacharyya参数作为一个代理的块错误概率的总和，并表明，存在一个通用的参数$μ$，使任何二进制无记忆对称信道$W$与容量$I(W)$，可靠的通信需要的速率，满足$R< I(W)-αN^{-\frac{1}μ}$，其中$α$是一个正常数和$N$是块长度。我们提供的$μ$，即$μ\geq 3.553$的下限，我们推测，确实$μ=3.627$，参数的二进制擦除通道。
英文摘要：
We consider the problem of determining the trade-off between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the block error probability, and show that there exists a universal parameter $μ$ such that for any binary memoryless symmetric channel $W$ with capacity $I(W)$, reliable communication requires rates that satisfy $R< I(W)-αN^{-\frac{1}μ}$, where $α$ is a positive constant and $N$ is the block-length. We provide lower bounds on $μ$, namely $μ\geq 3.553$, and we conjecture that indeed $μ=3.627$, the parameter for the binary erasure channel.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
