A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting

Algorithm 1

Error checking for decoding.

Input:

 The frozen nodes set, 𝕍_𝐹;

 The probability messages set of the 𝕍_𝐹;

 The matrixes, 𝐏_𝑁𝑀, 𝐀_𝐻𝐾 and 𝐁_𝑁;

Output:

 The error indicator vectors set, ℂ;

(1)  Getting 𝛾₀^𝑀−1 with the probability messages set of 𝕍_𝐹;

(2)  Getting 𝛾₀^𝐻−1 with 𝛾₀^𝑀−1 and 𝐏_𝑁𝑀;

(3)  for each 𝑣(𝑖,𝑗)∈𝕍_𝐹  do

(4)   if  𝑝_{𝑣(𝑖,𝑗)}(0)/𝑝_{𝑣(𝑖,𝑗)}(1)>𝛿  then

(5)    Setting the error indicator for each leaf node of 𝑣(𝑖,𝑗) to 0;

(6)   end if

(7)  end for

(8)  for each valid of 𝑐̂₀^𝐾−1  do

(9)   Getting 𝑐̂_𝐾^𝑁−1 with 𝐀_𝐻𝐾 and 𝛾₀^{𝑁−𝐾−1};

(10)  if (11) is satisfied then

(11)  Getting 𝑐₀^𝑁−1∈ℂ with 𝐁_𝑁;

(12)  else

(13)  Dropping the solution and continuing;

(14)  end if

(15) end for

(16) return  ℂ;