Decoding and Computing Algorithms for Linear Superposition LDPC Coded Systems

This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code. We focus on the design of decoding and computing algorithms. The main contributions of this paper include: 1) we present three types of iterative multistage decoding/computing algorithms, which are referred to as decoding-computing (DC) type, computing-decoding (CD) type and computing-decodingcomputing (CDC) type, respectively; 2) we propose a joint decoding/computing algorithm by treating the system as a nonbinary LDPC (NB-LDPC) coded system; 3) we propose a time-varying signaling scheme for multi-user communication channels. The proposed algorithms may find applications in superposition modulation (SM), multiple-access channels (MAC), Gaussian interference channels (GIFC) and two-way relay channels (TWRC). For SM system, numerical results show that 1) the proposed CDC type iterative multistage algorithm performs better than the standard DC type iterative multistage algorithm, and 2) the joint decoding/computing algorithm performs better than the proposed iterative multistage algorithms in high spectral efficiency regime. For GIFC, numerical results show that, from moderate to strong interference, the time-varying signaling scheme significantly outperforms the constant signaling scheme when decoded with the joint decoding/computing algorithm (about 8.5 dB for strong interference). For TWRC, numerical results show that the joint decoding/computing algorithm performs better than the CD type algorithm.