The velocity of the decoding wave for spatially coupled codes on BMS channels

We consider the dynamics of belief propagation decoding of spatially coupled Low-Density Parity-Check codes. It has been conjectured that after a short transient phase, the profile of “error probabilities” along the spatial direction of a spatially coupled code develops a uniquely-shaped wavelike solution that propagates with constant velocity ν. Under this assumption and for transmission over general Binary Memoryless Symmetric channels, we derive a formula for ν. We also propose approximations that are simpler to compute and support our findings using numerical data.