English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the dynamics of message passing for spatially coupled codes and,in particular, the set of density evolution equations that tracks the profileof decoding errors along the spatial direction of coupling. It is known that,for suitable boundary conditions and after a transient phase, the error profileexhibits a "solitonic behavior". Namely, a uniquely-shaped wavelike solutiondevelops, that propagates with constant velocity. Under this assumption wederive an analytical formula for the velocity in the framework of a continuumlimit of the spatially coupled system. The general formalism is developed forspatially coupled low-density parity-check codes on general binary memorylesssymmetric channels which form the main system of interest in this work. Weapply the formula for special channels and illustrate that it matches thedirect numerical evaluation of the velocity for a wide range of noise values. Apossible application of the velocity formula to the evaluation of finite sizescaling law parameters is also discussed. We conduct a similar analysis forgeneral scalar systems and illustrate the findings with applications tocompressive sensing and generalized low-density parity-check codes on thebinary erasure or binary symmetric channels.

The Velocity of the Propagating Wave for Spatially Coupled Systems with Applications to LDPC Codes