Acceleration of s-polar ecc throughput by scheduler

A method of simplified successive cancellation list (SSCL) error decoding of S-polar codes, comprising:

• generating a perfect binary tree with 2N−1 nodes based on an S-polar code of length N=2n, wherein n is a non-negative integer, and for an lth path in a list of L paths through the perfect binary tree, 1≤l≤L, wherein the S-Polar code is a generalized concatenated code (GCC) including Reed-Solomon (RS) codes as outer codes and polar codes as inner codes, wherein information is encoded into an N×J array using S−1 outer codes and S inner codes in S stages, and at each stage s of the S stages, information bits and parities from a previous outer code of a previous stage (s−1) are encoded into n=Kouts+1−Kouts codewords C(s) and stored as n rows of the array, C(s) being a codeword at stage s, Kouts representing an amount of data in an outer codeword at stage s, and the n rows of the array being mapped into a coset array in which an s+1th outer code for systematically encoding t=kouts−kouts+1 columns of the coset array, and parities of the encoded codewords being transmitted to a next inner code for encoding, wherein S and J are non-negative integers;
• receiving a vector of length 2n of log likelihood ratios (LLR), each entry of the vector being one of q possible values and L being a size of the list, wherein for a first layer of decoding, soft calculations in a left child of a root, vl, is a vector αi of length 2n-1 which takes values in a set of size q2, and soft calculations in a right child of the root vr is a vector αr of length 2n-1 with entries taking values in a set of size 2q2, wherein αr,i depends on a hard decision bit βl,I;
• based on 3q2f+N log2 q<<Nf, f being a number of bits that represent a soft calculation value, the method further comprises:
• determining a value of αl,i for coordinates 2i and 2i+1, for 0≤i<2n-1, by accessing a first lookup table of size q2;
• and
• determining a value of αr,i. by accessing a second lookup table of size 2q2,
• wherein for a second layer of decoding, a first node from a left has q4 possible values for soft calculations, a second node from the left has 2q4 possible values for soft calculations, a third node from the left has 4q4 for possible values for soft calculations, and a last node has 8q4 f possible values for soft calculations;
• and
• based on 15q4+N logq 2<<f N (L/2+1), the method further comprises:
• determining a value of αl,i for a leftmost node by accessing a third lookup table of size q4;
• determining a value of αl,i for a next leftmost node by accessing a fourth lookup table of size 2q4;
• determining a value of αl,i for a next rightmost node by accessing a fifth lookup table of size 4q4;
• and
• determining a value of αl,i for a rightmost node by accessing a sixth lookup table of size 8q4.