The near-Shannon-capacity performance of the Low-Density Parity-Check (LDPC) and turbo codes have rekindled the development of coding theory and great successes have been established for standard memoryless binary-input/symmetric-output channels. This talk will first provide a general overview of the two most important analysis tools in iterative decoding: the density evolution and the EXtrinsic InformaTion (EXIT) chart analysis. We will then discuss the difficulty of applying these existing techniques on non-symmetric memoryless channels. By complementing the asymptotic performance concentration theorem with a perfect projection convergence theorem, we generalize the density evolution method for non-symmetric channels. Some implications of our results include the stability conditions for non-symmetric channels, the local optimality of the belief propagation decoder, and the typicality of linear LDPC codes, which further justifies the usage of existing tools on non-symmetric channels. This new powerful technique successfully bridges the gap between symmetric channels and general memoryless channels, and will be demonstrated on a simple non-symmetric model for optical storage channels.

We also provide various finite-dimensional bounds on the decodable thresholds applicable to any memoryless channels, including the best bound for fading channels to date. These bounds confirm the uniform outstanding performance of LDPC codes on all channel models. Motivated by the Z_m-based performance bound, a bandwidth-efficient coded modulation is considered and near capacity performance is reported.

Chih-Chun Wang received the B.E. degree in electrical engineering from National Taiwan University, Taipei, Taiwan in 1999, and the M.S. degree in electrical engineering from Princeton University in 2002. He is a Ph.D. candidate in electrical engineering at Princeton University, Princeton, NJ. He worked in COMTREND Corporation, Taipei, Taiwan, from 1999-2000, and spent the summer of 2004 with Flarion Technologies, during which he was developing practical turbo equalization schemes for multiple antenna systems. His current research interests are in optimal control, communication theory, network information theory, and general coding theory, especially on iterative decoding on LDPC codes and algebraic codes.