Decoding and Turbo Equalization for LDPC Codes Based on Nonlinear Programming

Abstract

Decoding and Turbo Equalization (TEQ) algorithms based on the Sum-Product Algorithm (SPA) are well established for LDPC codes. However there is increasing interest in linear and nonlinear programming (NLP)-based decoders which may offer computational and performance advantages over the SPA. We present NLP decoders and Turbo equalizers based on an Augmented Lagrangian formulation of the decoding problem. The decoders update estimates of both the Lagrange multipliers and transmitted codeword while solving an approximate quadratic programming problem. Simulation results show that the NLP decoder performance is intermediate between the SPA and bit-flipping algorithms. The NLP may thus be attractive in some applications as it eliminates the tanh/atanh computations in the SPA.