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

This paper considers the performance of $(j,k)$-regular low-densityparity-check (LDPC) codes with message-passing (MP) decoding algorithms in thehigh-rate regime. In particular, we derive the high-rate scaling law for MPdecoding of LDPC codes on the binary erasure channel (BEC) and the $q$-arysymmetric channel ($q$-SC). For the BEC, the density evolution (DE) thresholdof iterative decoding scales like $\Theta(k^{-1})$ and the critical stoppingratio scales like $\Theta(k^{-j/(j-2)})$. For the $q$-SC, the DE threshold ofverification decoding depends on the details of the decoder and scales like$\Theta(k^{-1})$ for one decoder.  Using the fact that coding over large finite alphabets is very similar tocoding over the real numbers, the analysis of verification decoding is alsoextended to the the compressed sensing (CS) of strictly-sparse signals. A DEbased approach is used to analyze the CS systems with randomized-reconstructionguarantees. This leads to the result that strictly-sparse signals can bereconstructed efficiently with high-probability using a constant oversamplingratio (i.e., when the number of measurements scales linearly with the sparsityof the signal). A stopping-set based approach is also used to get stronger(e.g., uniform-in-probability) reconstruction guarantees.

On the Iterative Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing