Optimization of scaling soft information in iterative decoding via density evolution methods

Density evolution has recently been used to analyze iterative decoding and explain many characteristics of iterative decoding including convergence of performance and preferred structures for the constituent codes. The scaling of extrinsic information (messages) has been heuristically used to enhance the performance in the iterative decoding literature, particularly based on the min-sum message passing algorithm. In this paper, it is demonstrated that density evolution can be used to obtain the optimal scaling factor and also estimate the maximum achievable scaling gain. For low density parity check (LDPC (codes and serially) concatenated convolutional codes (SCCC) with two-state constituent codes, the analytic density evolution technique is used, while the signal-to-noise ratio (SNR) evolution technique and the EXIT chart technique is used for SCCC with more than 2 state constituent codes. Simulation results show that the scaling gain predicted by density evolution or SNR evolution matches well with the scaling gain observed by simulation.