This paper presents a low complexity optimized algorithm for design of bilayer lengthened LDPC(BL-LDPC) code for decode-and-forward relay system.The design is performed over the expanded graph of the BL-LDPC code,which consists of the original bilayer graph and the extra added relaygenerated parity check bits.To build up our proposed optimized algorithm,we present a modified Gaussian approximation algorithm for the expanded structure of the BL-LDPC code.Then using the proposed optimized algorithm,we find the optimum overall expanded graph of the BL-LDPC code.Simulation results show that the BL-LDPC codes obtained by our proposed optimized algorithm have excellent bit-error-rate performances and small gaps between the convergence thresholds and the theoretical limits when transmitted over the additive white Gaussian noise channels.
A multi-input multi-output(MIMO) separated two-way relay channel(STWRC) is considered,where two users exchange their messages via a relay node.When each link is quasi-static Rayleigh fading,the achievable diversity-multiplexing tradeoff(DMT) of the half-duplex STWRC is analyzed.Firstly,the achievable DMT of the STWRC with static decode-and-forward(DF) protocol is obtained.Then,a dynamic decode-and-forward(DDF) protocol for the STWRC is proposed,where the relay listening time varies dynamically with the channel qualities of the links between two users and the relay.Finally,the achievable DMT of the proposed DDF protocol is derived in a case-bycase manner.Numerical examples are also provided to verify the theoretical analysis of both protocols.
