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We consider the dynamics of belief propagation decoding of spatially coupledLow-Density Parity-Check codes. It has been conjectured that after a shorttransient phase, the profile of "error probabilities" along the spatialdirection of a spatially coupled code develops a uniquely-shaped wave-likesolution that propagates with constant velocity v. Under this assumption, andfor transmission over general Binary Memoryless Symmetric channels, we derive aformula for v. We also propose approximations that are simpler to compute andsupport our findings using numerical data.

The Velocity of the Decoding Wave for Spatially Coupled Codes on BMS Channels