Density Evolution is a simulative tool that models the behaviour of SPA (sum-product) decoders. It is useful because it enables the optimization of code designs so that extensive simulations can be avoided and code constructions that approach the channel capacity can be found relatively quickly. It has been applied extensively in the framework of classical communications to find LDPC codes that approach the Shannon limits of channels very closely ("On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit").

I am interested in applying this design optimization technique in the quantum paradigm, specifically to the work I am conducting on QLDPC codes. Although I'm fairly confident with regard to my understanding of density evolution itself and I believe I can transcend it (so to speak) to my QEC scenario, it would be of great aid to my research if I could get my hands on a small example or implemented version of the classical LDPC density evolution algorithm. I haven't been able to find much after a thorough web search, hence my posting of this question. In the absence of an example, I would also be grateful if I were to be directed towards publications regarding density evolution applied to LDPC codes.


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