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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Elementary trapping sets (ETSs) are the main culprits for the performance ofLDPC codes in the error floor region. Due to the large quantity, complexstructures, and computational difficulties of ETSs, how to eliminate dominantETSs in designing LDPC codes becomes a pivotal issue to improve the error floorbehavior. In practice, researchers commonly address this problem by avoidingsome special graph structures to free specific ETSs in Tanner graph. In thispaper, we deduce the accurate Tur\'an number of $\theta(1,2,2)$ and prove thatall $(a,b)$-ETSs in Tanner graph with variable-regular degree $d_L(v)=\gamma$must satisfy the bound $b\geq a\gamma-\frac{1}{2}a^2$, which improves the lowerbound obtained by Amirzade when the girth is 6. For the case of girth 8, bylimiting the relation between any two 8-cycles in the Tanner graph, we prove asimilar inequality $b\geq a\gamma-\frac{a(\sqrt{8a-7}-1)}{2}$. The simulationresults show that the designed codes have good performance with lower errorfloor over additive white Gaussian noise channels.

Theoretical Bounds for the Size of Elementary Trapping Sets by Graphic Methods