关于BICM容量
On the BICM Capacity
摘要：
最佳的二进制标记，输入分布，和输入字母的所谓的位交织编码调制（BICM）的能力进行了分析，特别注意低信噪比（SNR）制度。对于8进制脉冲幅度调制（PAM）和0.75比特/符号，折叠二进制码导致比二进制反射格雷码（BRGC）和自然二进制码（NBC）更高的容量。如果适当地选择输入符号分布，则可以几乎完全消除加性高斯白噪声（AWGN）容量和具有BRGC的BICM容量之间的1dB差距。一阶渐近的BICM容量为任意输入字母和分布，尺寸，均值，方差和二进制标签。这些渐近性用于定义BICM的一阶最优（FOO）星座，即使BICM达到香农极限$-1.59 \tr{dB}$的星座。它示出的$\Eb/N_0$所需的可靠传输在渐近低速率BICM可以高达无穷大，均匀的输入分布和8-PAM只有72类的二进制标号与不同的一阶渐近行为，这个数字减少到只有26个8进制相移键控（PSK）。对BICM的FOO星座问题也给出了一个一般性的回答：使用Hadamard变换，发现对于均匀输入分布，BICM的星座是FOO当且仅当它是超立方体的线性投影。基于PAM或正交幅度调制输入字母表的星座是FOO，当且仅当它们被NBC标记时;如果星座是基于PSK输入字母表的，如果输入字母表有四个以上的点，它永远不会是FOO，不管标记如何。
英文摘要：
Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit $-1.59 \tr{dB}$. It is shown that the $\Eb/N_0$ required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.
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。
