论文标题
在近似中，随机代码合奏的块误差概率的边界和精确计算
On Approximation, Bounding & Exact Calculation of Block Error Probability for Random Code Ensembles
论文作者
论文摘要
本文提出了一种计算某些随机代码集合的确切平均块误差概率在最大样本解码下的方法。所提出的方法适用于各种渠道和合奏。重点是在添加白色高斯噪声通道上的球形和高斯随机代码以及二进制对称通道和二元擦除通道上的二进制随机代码。 对于统一的球形合奏香农（Shannon），1959年在$ n $维空间中以坚实的角度进行了争论，但所介绍的方法将问题投入了两个维度，并应用了标准的三角学。这简化了派生，还允许分析独立的分布式（I.I.D.）高斯合奏，事实证明，对于短块长度和高速率，它的性能更好。此外，找到了均匀球形集合的平均块误差概率的新下限。对于具有三个以上代码字的代码，它比球形填料绑定更紧，但需要完全相同的计算工作。此外，提出了紧密的近似值，以简化确切的平均误差概率和两个边界的计算。 对于二进制对称通道和二元擦除通道，得出了I.I.D. \随机编码的平均块误差概率的边界，并将其与确切的计算进行了比较。
This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. The proposed method is applicable to various channels and ensembles. The focus is on both spherical and Gaussian random codes on the additive white Gaussian noise channel as well as binary random codes on both the binary symmetric channel and the binary erasure channel. While for the uniform spherical ensemble Shannon, in 1959, argued with solid angles in $N$-dimensional space, the presented approach projects the problem into two dimensions and applies standard trigonometry. This simplifies the derivation and also allows for the analysis of the independent identically distributed (i.i.d.) Gaussian ensemble which turns out to perform better for short blocklengths and high rates. Moreover, a new lower bound on the average block error probability of the uniform spherical ensemble is found. For codes with more than three codewords, it is tighter than the sphere packing bound, but requires exactly the same computing effort. Furthermore, tight approximations are proposed to simplify the computation of both the exact average error probability and the two bounds. For the binary symmetric channel and the binary erasure channel, bounds on the average block error probability for i.i.d.\ random coding are derived and compared to the exact calculations.
