Special node (constituent code) processing for fast/simplified polar successive cancellation list (SCL) decoder

1. An apparatus for constituent code processing in polar successive cancellation list (SCL) decoding, comprising:

a processor configured to:

determine an activation value I and a number r, where I is a binary value and r is an integer, (I, r)=ƒ(R, k, m), ƒ is a function, R is a number indicating node reliability, k is an integer indicating a number of information nodes, and m is an integer indicating a number of leaf nodes;

determine q indices min 1 , min 2 , . . . , min q of least reliable bits in the constituent code, wherein q is a number;

determine r candidate paths;

determine path metrics PM t j of a codeword j for each candidate path t; and

select r most probable paths based on PM t j .

2. The apparatus of claim 1 , wherein the constituent code is an intermediate node corresponding to a constituent polar code structure called a special node.

3. The apparatus of claim 2 , wherein the special node is a single parity check (SPC) code.

4. The apparatus of claim 1 , wherein a number of least reliable bits in h(α v [i]) is equal to q, h(α v [i]) is a hard decision of α v [i], α v is a vector of length m that indicates log-likelihood ratios of node v, and i and j are integers.

5. The apparatus of claim 2 , wherein R is characterized by node location.

6. The apparatus of claim 4 , wherein the processor is further configured to determine the q indices min 1 , min 2 , . . . , min q based on α v , wherein α v [min 1 ]≤α v [min 2 ]≤ . . . ≤α v [min q ].

7. The apparatus of claim 4 , wherein the number q is equal to a number of minimum elements found in |α v |, wherein α v is a vector of length m that indicates log-likelihood ratios of node v.

8. The apparatus of claim 4 , wherein the potential codeword j of the node v is obtained by flipping binary values of combinations of q least reliable bits in h(α v [i]) based on α v such that a constraint imposed by a distribution of the k information nodes is satisfied, wherein h(α v [i]) is a hard decision of α v [i], α v is a vector of length m that indicates log-likelihood ratios of node v, and i is an integer.

9. The apparatus of claim 4 , wherein each candidate path t is associated with a path metric PM t , wherein PM t =PM s −Σ i |β t [i]−h(α v [i])|×|α v [i]|, where PM s is an incoming path metric, β t is a candidate codeword of the node v, and PM t indicates a reliability of the candidate path t.

10. The apparatus of claim 1 , wherein I is determined based on location of a node.

11. A method of constituent code processing for polar successive cancellation list (SCL) decoding, comprising:

determining an activation value I and a number r, where I is a binary value and r is an integer, (I, r)=ƒ(R, k, m), ƒ is a function, R is a number indicating node reliability, k is an integer indicating a number of information nodes, and m is an integer indicating a number of leaf nodes;

determining q indicies min 1 , min 2 , . . . , min q of least reliable bits in the constituent code, wherein q is a number;

determining r candidate paths;

determining path metrics PM t j of a codeword j for each candidate path t; and

selecting r most probable paths based on PM t j .

12. The method of claim 11 , wherein the constituent code is an intermediate node corresponding to a constituent polar code structure called a special node.

13. The method of claim 12 , wherein the special node is a single parity check (SPC) code.

14. The method of claim 11 , wherein a number of least reliable bits in h(α v [i]) is equal to q, {min j } are indices of the q least reliable bits; h(α v [i]) is a hard decision of α v [i], α v is a vector of length m that indicates log-likelihood ratios of node v, and i and j are integers.

15. The method of claim 12 , wherein R is characterized by node location.

16. The method of claim 14 , wherein determining the q indices min 1 , min 2 , . . . , min q is comprised of determining the q indices min 1 , min 2 , . . . , min q based on α v , wherein α v [min 1 ]≤α v [min 2 ]≤ . . . ≤α v [min q ].

17. The method of claim 14 , wherein the number q is equal to a number of minimum elements found in |α v |, wherein α v is a vector of length m that indicates log-likelihood ratios of node v.

18. The method of claim 14 , wherein the codeword j of node v is obtained by flipping binary values of combinations of q least reliable bits in h(α v [i]) based on α v such that a constraint imposed by a distribution of the k information nodes is satisfied, wherein h(α v [i]) is a hard decision of α v [i], α v is a vector of length m that indicates log-likelihood ratios of node v, and i is an integer.

19. The method of claim 14 , wherein each candidate path t is associated with a path metric PM t , wherein PM t =PM s −Σ i |β t [i]−h(α v [i])|×|α v [i]|, where PM s is an incoming path metric, β t is a candidate codeword of the node v, and PM t indicates a reliability of the candidate path t.

20. The method of claim 11 , wherein I is determined based on location of a node.