Superposition Mapping: Theory and Applications

• Applicant: Professor Dr.-Ing. Peter A. Höher
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2010 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 188321379

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.

• DFG Programme: Research Grants