Journal of Electrical and Computer Engineering

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 𝑖 fi x e d = 1 , … , 𝑁
  Set π‘š m i n = ∞ .
  Set πœ’ = { 𝑖 fi x e d } .
  while π‘š m i n > 0 . 0
    for 𝑖 = 1 , … , 𝑁
    -Set ⋃ πœ’ = πœ’ { 𝑖 } .
    -Set πœ† π‘˜ = 0 . 0 for all π‘˜ ∈ πœ’ .
    -Set πœ† π‘˜ = 1 . 0 for all π‘˜ ∈ 𝑉 ⧡ πœ’ .
    -Perform MS Decoding for β„“ iterations.
     if  m i n 𝑗 = 1 , … , 𝑁 π‘š 𝑣 𝑗 < π‘š m i n
       -Set π‘š m i n = m i n 𝑗 = 1 , … , 𝑁 π‘š 𝑣 𝑗 .
       -Set 𝑗 m i n = a r g m i n 𝑗 = 1 , … , 𝑁 π‘š 𝑣 𝑗 .
      end
     -Set β‹‚ ⋃ πœ’ = πœ’ ( { 𝑉 ⧡ { 𝑖 } } { 𝑖 fi x e d } ) .
     end
    -Set ⋃ πœ’ = πœ’ { 𝑗 m i n } .
    -Create a binary vector v with 𝑣 π‘˜ = 1 if π‘˜ ∈ πœ’ , and
       𝑣 π‘˜ = 0 if π‘˜ ∈ 𝑉 ⧡ πœ’ .
    -Compute the integar syndrome 𝐬 i n t = 𝐻 𝐯 𝑇 .
    -Compute the binary syndrome 𝐬 b i n = 𝐻 𝐯 𝑇 with
      Hamming weight 𝑀 𝑠 .
    -Compute the integar vector 𝐳 = 𝐻 𝑇 𝐬 b i n
     if  m i n π‘˜ = 1 , … , 𝑀 𝑠 i n t , π‘˜ β‰₯ 2
        πœ’ is a ( | πœ’ | , 𝑀 𝑠 ) Stopping Set.
    end
     πœ’ is a ( | πœ’ | , 𝑀 𝑠 ) Trapping Set.
    if  𝑧 π‘˜ 𝑑 < ⌊ 𝑣 π‘˜ 2 βŒ‹ for all π‘˜ ∈ πœ’
          πœ’ is a ( | πœ’ | , 𝑀 𝑠 ) Absorbing Set.
    end
    if   𝑧 π‘˜ 𝑑 < ⌊ 𝑣 π‘˜ 2 βŒ‹ for all π‘˜ = 1 , … , 𝑁
         πœ’ is a ( | πœ’ | , 𝑀 𝑠 ) Fully Absorbing Set.
    end
  end
end