Comparison with Multilevel Coding hil MLCwith MSD achieves the od mdulation capacity,it does not achieve the coded modulation error exponent.This is due to the MLC (with or without MSD)error exponent always being given by the minimum of the error exponents of the various levels, which results in an error exponent smaller than 1.While BICM suffers from a nonzero,yet small,capacity loss compared to CM and MLC/MSD,BICM attains a larger error exponent, whose los with respect to CM is small.This loss may be large for ar MLC construction.In general,the decoding complexity of BICM is larger than that of MLC/MSD,since the codes of MLC are shorter.One such example is a code where only a few bits out of the m are coded while the rest are left uncoded.In practice,however,if the decoding complexity grows linearly with the number of bits in a codeword,e.g,with LDPC or turbo codes,the overall complexity of BICM becomes comparable to that of MLC/MSD. Summary:Since its introduction,BICM has been regarded as a pragmatic yet powerful scheme to achieve high data rates with general signal constellations.Nowadays,BICM is employed in a wide range of practical communication systems,such as DVB-S2,Wireless LANs.DSL.WiMax.and the 4G cellular systems 5.12 Q-ary LDPC-coded Modulations 5b9C9g的2D信号集，最好的系统性能最多只能达到 -,而此极限距离Shannon容量限还有1dB左右的差距。Toachieve the Shannon-capacity-approaching performance (in the high SNR regime)for coded-modulation systems,it is necessary to use constellation shaping in conjunction with coding.Modern channel coding techniques are subjects of the previous chapters,and the related shaping methods are discussed below 5.13.1 Overview of Constellation Shaping Methods 从前面关于成形增益的讨论中，我们知道信号星座成形基本上有两种技术： ●第一种我们称为几何成形，使信号星座的几何形状类似于球体（在高维信号空间中）： 。第二种我们称为概率成形，使发送的信号具有与正态分布相近的分布。 在编码调制系统中具体实现时，这两种成形技术可以有多种实现方法，但大体上可 以分为两大类：单层编码与两层编码方法。 在两层方案中[Forney84],一层为信道编码，另一层为信源编码（成形编码）.图5.13.1 所示是编码与成形结合的两层方案。首先把一个给定的-维信号星座A划分成若干个信 号点子集A,1s1sm。二进制数据流u按照一定的速率划分为两个子数据流和。 子数据流进入一个信道编码器，输出的序列(c1,.,9.,c)用来选择信号子集序列 (51,.N,其中号，∈{4,1siSm。这一层称为信道编码层。子数据流业进入 个成形编码器，输出的序列用来选择一个特定的信号点序列(x,x。xw,其中x 2828 Comparison with Multilevel Coding: While MLC with MSD achieves the coded modulation capacity, it does not achieve the coded modulation error exponent. This is due to the MLC (with or without MSD) error exponent always being given by the minimum of the error exponents of the various levels, which results in an error exponent smaller than 1. While BICM suffers from a nonzero, yet small, capacity loss compared to CM and MLC/MSD, BICM attains a larger error exponent, whose loss with respect to CM is small. This loss may be large for an MLC construction. In general, the decoding complexity of BICM is larger than that of MLC/MSD, since the codes of MLC are shorter. One such example is a code where only a few bits out of the m are coded while the rest are left uncoded. In practice, however, if the decoding complexity grows linearly with the number of bits in a codeword, e.g., with LDPC or turbo codes, the overall complexity of BICM becomes comparable to that of MLC/MSD. Summary: Since its introduction, BICM has been regarded as a pragmatic yet powerful scheme to achieve high data rates with general signal constellations. Nowadays, BICM is employed in a wide range of practical communication systems, such as DVB-S2, Wireless LANs, DSL, WiMax, and the 4G cellular systems. 5.12 Q-ary LDPC-coded Modulations 5.13 Combined Coding and Shaping 从图 5.1.7 可知，采用均匀的 2D 信号集，最好的系统性能最多只能达到 constrained-capacity，而此极限距离 Shannon 容量限还有 1dB 左右的差距。To achieve the Shannon-capacity-approaching performance (in the high SNR regime) for coded-modulation systems, it is necessary to use constellation shaping in conjunction with coding. Modern channel coding techniques are subjects of the previous chapters, and the related shaping methods are discussed below. 5.13.1 Overview of Constellation Shaping Methods 从前面关于成形增益的讨论中，我们知道信号星座成形基本上有两种技术： z 第一种我们称为几何成形，使信号星座的几何形状类似于球体（在高维信号空间中）； z 第二种我们称为概率成形，使发送的信号具有与正态分布相近的分布。 在编码调制系统中具体实现时，这两种成形技术可以有多种实现方法，但大体上可 以分为两大类：单层编码与两层编码方法。 在两层方案中[Forney84]，一层为信道编码，另一层为信源编码（成形编码）。图 5.13.1 所示是编码与成形结合的两层方案。首先把一个给定的 n-维信号星座A 划分成若干个信 号点子集Ai ，1 ≤ i ≤ m 。二进制数据流 u 按照一定的速率划分为两个子数据流 u(c) 和 u(s) 。 子数据流 u(c) 进入一个信道编码器，输出的序列 c=(c1,.,cj,.,cL)用来选择信号子集序列 s=(s1,.,st,.,sN)，其中 { ,1 } t i s im ∈ ≤≤ A 。这一层称为信道编码层。子数据流 u(s) 进入一 个成形编码器，输出的序列用来选择一个特定的信号点序列 x=(x1,.,xt,.,xN)，其中 xt