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 indices min 1 , min 2 , . . . , min q of q least reliable bits in a constituent code, wherein q is an integer;

determine candidate paths;

determine path metrics PM t j of a codeword j for each candidate path t based on one or more of the q indices min 1 , min 2 , . . . , min q ; and

select r most probable paths based on the path metrics PM t j , wherein r is an integer,

wherein a number of least reliable bits in a hard decision h(a v [i]) of a v [i] is equal to q, and

wherein a v [i] is a vector of length m that indicates log-likelihood ratios of node v and i, j, and m are integers.

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 one of the number of least reliable bits of h(a v [i]) is flipped.

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

6. The apparatus of claim 1 , wherein the number q is equal to a number of minimum elements found in |a v |, wherein a v is a vector of length m that indicates log-likelihood ratios of node v.

7. The apparatus of claim 1 , wherein the potential codeword j of the node v is obtained by flipping binary values of combinations of q least reliable bits in h(a v [i]) based on a v such that a constraint imposed by a distribution of k information nodes is satisfied, wherein h(a v [i]) is a hard decision of a v [i], a v , is a vector of length m that indicates log-likelihood ratios of node v, and i and k are integers.

8. The apparatus of claim 1 , wherein each candidate path t is associated with a path metric PM t , wherein PM t =PM s −Σ i |β t [i]−h(a v [i])|×|a 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.

9. The apparatus of claim 1 , wherein a least reliable two bits of h(a v [i]) are flipped.

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

determining indices min 1 , min 2 , . . . , min q of q least reliable bits in a constituent code, wherein q is an integer;

determining candidate paths;

determining path metrics PM t j of a codeword j for each candidate path t based on one or more of the q indices min 1 , min 2 , . . . , min q ; and

selecting r most probable paths based on the path metrics PM t j , wherein r is an integer,

wherein a number of least reliable bits in a hard decision h(a v [i]) of a v [i] is equal to q, and

wherein {min j } are indices of the q least reliable bits; and wherein a v [i] is a vector of length m that indicates log-likelihood ratios of node v, and i, j, and m are integers.

11. The method of claim 10 , wherein the constituent code is an intermediate node corresponding to a constituent polar code structure called a special node.

12. The method of claim 11 , wherein the special node is a single parity check (SPC) code.

13. The method of claim 10 , wherein one of the number of least reliable bits of h(a v [i]) is flipped.

14. The method of claim 10 , 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 a v , wherein a v [min 1 ]≤a v [min 2 ]≤ . . . ≤a v [min q ].

15. The method of claim 10 , wherein the number q is equal to a number of minimum elements found in |a v |, wherein a v is a vector of length m that indicates log-likelihood ratios of node v.

16. The method of claim 10 , wherein the codeword j of node v is obtained by flipping binary values of combinations of q least reliable bits in h(a v [i]) based on a v such that a constraint imposed by a distribution of k information nodes is satisfied, wherein h(a v [i]) is a hard decision of a v [i], a v is a vector of length m that indicates log-likelihood ratios of node v, and i and k an integers.

17. The method of claim 10 , wherein each candidate path t is associated with a path metric PM t , wherein PM t =PM s −E i |β t [i]−h(a v [i])|×|a 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.

18. The method of claim 10 , wherein a least reliable two bits of h(a v [i]) are flipped.