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

Algorithm 2

Decoding algorithm based on error checking and correcting.

Input:

 The the received vector 𝑦₀^𝑁−1;

Output:

 The decoded codeword, 𝑢₀^𝑁−1;

(1) Getting the probability messages 𝑞₀^𝑁−1(0) and 𝑞₀^𝑁−1(1) with the received vector 𝑦₀^𝑁−1;

(2) Getting the probability messages of each frozen node 𝕍_𝐹;

(3) Getting the error indicator vectors set ℂ with the Algorithm 1;

(4) for each 𝑐_𝑘⃗∈ℂ  do

(5)  Correcting the errors indicated by 𝑐_𝑘⃗ with (26);

(6)  Recalculating the probability messages of all the nodes of the decoder;

(7) end for

(8) Getting the optimal error indicator vector for the decoding;

(9) Getting the decoded codeword 𝑢₀^𝑁−1 by hard decision;

(10) return  𝑢₀^𝑁−1;