Velocity Analysis of BP Decoding Waves for SC-LDPC Ensembles on BMS Channels: An Interpolation-Based Approach

This paper is concerned with the dynamics of spatially-coupled low-density parity-check (SC-LDPC) ensembles for transmission on general binary memoryless symmetric (BMS) channels under belief-propagation (BP) decoding. The decoding waves of such ensembles are found to exhibit solitonic behavior, propagating along the Tanner graphs at asymptotically constant velocities. A low-complexity approach termed interpolated density evolution (IDE) is proposed to predict the decoding wave velocities. In this approach, the densities of a decoding wave are approximated by interpolating between some fixed points of an uncoupled DE recursion with one-dimensional functions. Two transfer functions for updating these interpolation functions in the IDE recursion are established and a simple strategy is introduced to deal with the coexistence of multiple transition regions. In addition, a threshold analysis is developed based on two ansatzes, explaining why our approach can achieve a good trade-off between computational cost and accuracy, as illustrated with some numerical examples at the end of this paper.