Superposition Mapping: Theory and Applications

众所周知，当且仅当信道输出是高斯分布时，才能实现高斯信道的容量。在高信噪比（SNRs）下，传统的映射方案（如QAM）无法达到香农极限。为了解决这个问题，在20世纪90年代，人们提出了信号整形技术，将均匀的符号分布转换为类高斯分布。叠加映射（SM）是指利用线性叠加将多个比特加载到适合数据传输的信道符号上的一类映射技术。当试图接近高信噪比区域的信道容量时，SM是信号整形的一个有吸引力的替代方案，特别是与接收端的迭代（涡轮）处理相结合。在项目的前两年，详细研究了以下任务：提出了一种新的功率分配方案，称为分组功率分配（GPA）。GPA是平等权力分配（EPA）和不平等权力分配（UPA）的结合。从符号分布和熵的角度对三种功率分配方案进行了比较。结果表明，所提出的功率分配方法在提高符号熵的同时，又能充分保持符号的高斯分布。此外，还将低密度混合校验码的概念应用于SM-GPA。采用一种新颖的两步退出图分析方法，对LDHC-SM-GPA的学位分配进行了优化。此外，SM已经与最先进的信号整形技术进行了比较。与信号整形不同，SM完全通过映射来实现高斯分布信号，从而避免了在发送端使用顺序整形技术的额外成本。此外，传统的整形技术在接收端难以获得符号位的软信息，这限制了其在迭代处理情况下的应用。对于OFDM传输，采用填充水的叠加映射来逼近信道容量。LDHC编码已经适应了这种系统。对LDHC码的度分布和度分配进行了修改，使之与动态位分配相匹配。蒙特卡罗仿真结果表明，在相同带宽效率下，LDHC-SM-OFDM优于LDPC-QAM-OFDM。根据目前的结果，有理由相信SM也能够接近MIMO信道的容量。第三年，重点是将LDHC编码应用于SM-MIMO传输。发射/接收天线数对LDHC码最优度分布和度分配的影响值得深入研究。

It is well known that the capacity of a Gaussian channel can be achieved if and only if the channel outputs are Gaussian distributed. At high signal-to-noise ratios (SNRs), conventional mapping schemes (like QAM) are not capable to achieve the Shannon limit. To solve this problem, in the 1990s signal shaping techniques have been proposed that transform a uniform symbol distribution into a Gaussian-like one. Superposition mapping (SM) refers to a class of mapping techniques which uses linear superposition to load multiple bits onto a channel symbol suitable for data transmission. SM is an attractive alternative to signal shaping when trying to approach the channel capacity in the high SNR region, particularly in conjunction with iterative (turbo) processing at the receiver side.During the first two years of the project, the following tasks have been investigated in detail:A new power allocation scheme, termed grouped power allocation (GPA), has been proposed. GPA is a combination of equal power allocation (EPA) and unequal power allocation (UPA). A comparison between these three power allocation schemes in terms of symbol distribution and entropy has been carried out. The results show that the proposed power allocation can boost the symbol entropy and meanwhile keeping the symbol distribution sufficiently Gaussian-like. Furthermore, the concept of low-density hybrid-check (LDHC) codes has been applied to SM-GPA. The degree allocation of LDHC-SM-GPA has been optimized by employing a novel two-step EXIT chart analysis. Additionally, SM has been compared with state-of-the-art signal shaping techniques. Different from signal shaping, SM accomplishes a Gaussian distributed signal purely by mapping, thus avoiding the additional cost for a sequence-wise shaping techniques at the transmitter side. Besides, for traditional shaping techniques it is computationally challenging to obtain soft information for the sign bits at the receiver side, which limits its application in the case of iterative processing. For OFDM transmission, superposition mapping with waterfilling has been applied to approach the channel capacity. LDHC coding has been adapted to this kind of system. The degree distribution and the degree allocation of LDHC codes have been modified to match the dynamic bit allocation. Monte Carlo simulation results show that LDHC-SM-OFDM outperforms LDPC-QAM-OFDM given the same bandwidth Efficiency. Based on the current results, it is reasonable to believe that SM is also able to approach the capacity of MIMO channels. In the third year, the focus shall be on applying LDHC coding to SM-MIMO transmission. The influence of the number of transmit/receive antennas on the optimal degree distribution and degree allocation of LDHC codes deserves to be an interesting topic for detailed investigations.