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The minimum pseudoweight is an important parameter related to the decodingperformance of LDPC codes with iterative message-passing decoding. In thispaper, we consider ensembles of periodically time-varying spatially coupledLDPC (SC-LDPC) codes and the pseudocodewords arising from their finite graphcovers of a fixed degree. We show that for certain $(J,K)$-regular SC-LDPC codeensembles and a fixed cover degree, the typical minimum pseudoweight of theunterminated (and associated tail-biting/terminated) SC-LDPC code ensemblesgrows linearly with the constraint (block) length as the constraint (block)length tends to infinity. We prove that one can bound the the freepseudodistance growth rate over a BEC from below (respectively, above) usingthe associated tail-biting (terminated) SC-LDPC code ensemble and showempirically that these bounds coincide for a sufficiently large period, whichgives the exact free pseudodistance growth rate for the SC-LDPC ensembleconsidered.

Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC