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...paper we apply Lyapunov’s classic theory [1] to the case of spatially coupled information processing systems, and show that the recently proposed “potential functions” used in the proofs in [2], [3], =-=[4]-=- are, in fact, an example from a wide class of Lyapunov functions. Such a systematic approach to the problem provides a general tool to deal with the dynamics of spatial coupling. The required definit...

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...he potential function, in the form defined in [4], does not exist for nonbinary LDPC codes. This fact motived us to study the existence of the potential function for a vector sparse system as in [4], =-=[11]-=- in the general case. In the last part of the paper, we show how to derive the potential function for any vector sparse system [4], [11] and develop some existence conditions. The remainder of the pap...

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...BP threshold of nonbinary SC-LDPC codes on the BEC to the so called potential threshold, which is conjectured to coincide with the MAP threshold. Our proof is based on the proof technique proposed in =-=[6, 7]-=- to prove threshold saturation for (binary) SC-LDPC codes. This technique is based on the Research supported by the Swedish Research Council under grant #20115961, the Swedish Foundation for Strategic...

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...shold saturation, theoretical analyses have been performed for general SC systems with one-dimensional coupling [9]–[11]. The methodologies are classified into those based on potential functions [9], =-=[10]-=- and on extrinsic information transfer (EXIT) functions [11]. Potential functions were also used for the analysis of threshold saturation in [7], [8]. The potentialbased methodology has the advantage ...