An Efficient Procedure for Bilayer-Expurgated LDPC Codes Design in Cooperative Relay Channels

作者：Mehrizi Sajad^*; Khosravi Sara; Ahmadian Mahmoud

来源：IEEE Communications Letters, 2017, 21(10): 2114-2117.

DOI：10.1109/LCOMM.2017.2708699

• Bilayer-expurgated LDPC codes
• relay channel
• density evolution
• code optimization
• sum of square polynomials

This letter proposes a fast optimization procedure to design bilayer-expurgated low density parity check codes in the relay channel. The code optimization problem aims to maximize the code rate while guaranteeing the convergence of the density evolution relations in upper and lower layer codes. The original problem is linear programming. Nevertheless, it suffers from high computational complexity, as it is semi-infinite programming (SIP) in a 2-D continuous interval. To efficiently solve it, we first approximate the density evolutions by polynomials. Then, leveraging optimization problems over the solution of sum of square multivariate polynomials the problem is transformed to semi-definite programming (SDP), where the global solution can be found efficiently using available SDP solvers. Our simulation shows that our approach results in significantly lower computational complexity with respect to the well-known method of quantization for solving the SIP problem, while both achieve the same performance.

• 出版日期2017-10