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Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC
The minimum pseudoweight is an important parameter related to the decoding
performance of LDPC codes with iterative message-passing decoding. In this
paper, we consider ensembles of periodically time-varying spatially coupled
LDPC (SC-LDPC) codes and the pseudocodewords arising from their finite graph
covers of a fixed degree. We show that for certain -regular SC-LDPC code
ensembles and a fixed cover degree, the typical minimum pseudoweight of the
unterminated (and associated tail-biting/terminated) SC-LDPC code ensembles
grows linearly with the constraint (block) length as the constraint (block)
length tends to infinity. We prove that one can bound the the free
pseudodistance growth rate over a BEC from below (respectively, above) using
the associated tail-biting (terminated) SC-LDPC code ensemble and show
empirically that these bounds coincide for a sufficiently large period, which
gives the exact free pseudodistance growth rate for the SC-LDPC ensemble
considered.Comment: 5 pages, 1 figure, accepted to 2018 IEEE Information Theory Workshop
(ITW) and to be published in the proceeding