Research Article

# The Manifestation of Stopping Sets and Absorbing Sets as Deviations on the Computation Trees of LDPC Codes

## Algorithm 1

Iterative problematic trapping set finder.
 for π ο¬ x e d = 1 , β¦ , π β Set π m i n = β . β Set π = { π ο¬ x e d } . β while π m i n > 0 . 0 ββββfor π = 1 , β¦ , π ββββ-Set β π = π { π } . ββββ-Set π π = 0 . 0 for all π β π . ββββ-Set π π = 1 . 0 for all π β π β§΅ π . ββββ-Perform MS Decoding for β iterations. βββββifβ m i n π = 1 , β¦ , π π π£ π < π m i n βββββββ-Set π m i n = m i n π = 1 , β¦ , π π π£ π . βββββββ-Set π m i n = a r g m i n π = 1 , β¦ , π π π£ π . ββββββend βββββ-Set β β π = π ( { π β§΅ { π } } { π ο¬ x e d } ) . βββββend ββββ-Set β π = π { π m i n } . ββββ-Create a binary vector v with π£ π = 1 if π β π , and ββββββ π£ π = 0 if π β π β§΅ π . ββββ-Compute the integar syndrome π¬ i n t = π» π― π . ββββ-Compute the binary syndrome π¬ b i n = π» π― π with ββββββHamming weight π€ π  . ββββ-Compute the integar vector π³ = π» π π¬ b i n ββββ ifβ m i n π = 1 , β¦ , π π  i n t , π β₯ 2 βββββββ π is a ( | π | , π€ π  ) Stopping Set. ββββend ββββ π is a ( | π | , π€ π  ) Trapping Set. ββββifβ π§ π π < β π£ π 2 β for all π β π βββββββββ π is a ( | π | , π€ π  ) Absorbing Set. ββββend ββββif β π§ π π < β π£ π 2 β for all π = 1 , β¦ , π ββββββββ π is a ( | π | , π€ π  ) Fully Absorbing Set. ββββend ββend end

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