Design of complexity-optimized raptor codes for BI-AWGN channel

Abstract

This paper aims to design a class of Raptor codes with optimized complexity for the binary input additive white Gaussian noise (BI-AWGN) channel under the joint decoding framework in which soft information is exchanged between the pre-code and the LT code iteratively. Utilizing the belief propagation (BP) decoder, the decoding complexity is measured by the average number of arithmetic operations needed to correctly recover each information bit. Based on the analytical asymptotic convergence analysis which is built upon extrinsic information transfer (EXIT) charts, we develop a numerical approximation for the number of iterations needed for measuring the decoding complexity, and then formulate an optimization problem for the design of efficient output degree distributions. We further discuss the fundamental problem of complexity-rate tradeoff in Raptor code design. Simulations show that the optimized distribution indeed achieves lower complexity without much performance loss compared to other existing rate-optimized Raptor Codes.