Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images

In this paper, a method to design regular (2, d_c)- LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes.     

Analysis and optimization of irregular LDPC codes for joint source-channel decoding

In this paper, we present a characterization, through its convergence analysis, and an optimisation of a joint source-channel receiver composed of a LDPC decoder and a Soft Input Soft Output (SISO) source decoder. Under Gaussian approximation, assuming the knowledge of the extrinsic mutual information transfer function (EXIT chart) of the source decoder, we derive the Mutual Information evolution equations, that semianalytically describe the convergence of the iterative system behavior and, to complete the study, the stability condition at the convergence fixed point is derived for the joint receiver. From this analysis, a general optimisation method of the irregularity of the LDPC codes is proposed, which can be reduced to a linear programming optimisation problem. Simulation results show improved performance when compared to an AWGN optimized LDPC code.