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The Velocity of the Propagating Wave for General Coupled Scalar Systems (1701.03759v1)
Published 13 Jan 2017 in cs.IT and math.IT
Abstract: We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction problems. Assuming that the "profile" describing the average state of the algorithm exhibits a solitonic wave-like behavior after initial transient iterations, we derive a formula for the propagation velocity of the wave. We illustrate the formula with two applications, namely Generalized LDPC codes and compressive sensing.