Devices and methods for constructing polar like codes
A method for constructing Polarization Assisted Convolutional (PAC) codes, the method including passing a codeword through a noisy channel to obtain a first bit and a noise value, determining whether the first bit is an information bit or a non-information bit based on the noise value by decoding the codeword to obtain a decoded codeword, selecting at least one of a reward or a penalty for the first bit based on the decoded codeword, the reward being set based on a probability of decoding, and the selecting selects the penalty for the first bit in response to determining the first bit is incorrectly decoded, and iterating the passing, the determining and the selecting according to Q-values for each state among a plurality of states, at least one of the Q-values corresponding to the first bit.
1. A method for constructing at least one Polarization Assisted Convolutional (PAC) code, the method comprising:
passing, by processing circuitry, at least one codeword among a plurality of codewords through a noisy channel to obtain a first bit and a noise value;
determining, by the processing circuitry, whether the first bit is an information bit or a non-information bit based on the noise value by decoding the at least one codeword to obtain at least one decoded codeword;
selecting, by the processing circuitry, at least one of a reward or a penalty for the first bit based on the at least one decoded codeword, the reward being set based on a probability of decoding, and the selecting selects the penalty for the first bit in response to determining the first bit is incorrectly decoded; and
iterating the passing, the determining and the selecting, by the processing circuitry, according to Q-values for each state among a plurality of states, at least one of the Q-values corresponding to the first bit.
2. The method as claimed in claim 1 , wherein each of the plurality of codewords comprises an uncoded data length (K), a code rate (K/N, where N is a code word length) and a precoder.
3. The method as claimed in claim 1 , wherein the method further comprises:
performing, by the processing circuitry, a Q-learning method for constructing the at least one PAC code.
4. The method as claimed in claim 1 , wherein the determining whether the first bit is the information bit or the non-information bit comprises:
sorting Reed-Muller (RM) scores of N information bit indices in an ascending order, N being a length of a first codeword among the at least one codeword, and
dividing the N information bit indices into a plurality of subsets.
5. The method as claimed in claim 4 , wherein
the plurality of subsets comprises a first subset of indices, a second subset of indices, and a third subset of indices, the first subset of indices having an RM score less than a boundary RM score, the second subset of indices having an RM score greater than the boundary RM score, and the third subset of indices having an RM score equal to the boundary RM score; and
the method further comprises:
allocating the first subset of indices to a frozen set,
allocating the second subset of indices to a set of information bit indices, and
selecting an action for the third subset of indices based on a current state among the plurality of states and a policy.
6. The method as claimed in claim 5 , further comprising:
updating a value function of a current state action pair based on the selecting at least one of the reward or the penalty; and
updating a respective value function of all state action pairs taken during an episode based on termination of the episode or removal of all zero codewords among the plurality of codewords from a list.
7. The method as claimed in claim 1 , further comprising:
selecting, by the processing circuitry, one bit index in each iteration for which a corresponding PAC code achieves a minimum Hamming distance.
8. The method as claimed in claim 1 , wherein the selecting at least one of the reward or the penalty comprises:
allocating a reward in response to determining that the first bit is correctly decoded; and
a partial reward or a partial penalty based on a position of all zero codewords among the plurality of codewords in a list.
9. A device for constructing at least one polarization assisted convolutional (PAC) code, the device comprising:
processing circuitry configured to:
pass at least one codeword among a plurality of codewords through a noisy channel to obtain a first bit and a noise value,
determine whether the first bit is an information bit or a non-information bit based on the noise value by decoding the at least one codeword to obtain at least one decoded codeword,
select at least one of a reward or a penalty for the first bit based on the at least one decoded codeword, the reward being set based on a probability of decoding, and the selection includes selecting the penalty for the first bit in response to determining the first bit is incorrectly decoded, and
iterate the pass of the at least one codeword, the determination of whether the first bit is the information bit or the non-information bit and the selection of at least one of the reward or the penalty according to Q-values for each state among a plurality of states, at least one of the Q-values corresponding to the first bit.
10. The device as claimed in claim 9 , wherein each of the plurality of codewords comprises an uncoded data length (K), a code rate (K/N, where N is a code word length) and a precoder.
11. The device as claimed in claim 9 , wherein the processing circuitry is configured to perform a Q-learning method for constructing the at least one PAC code.
12. The device as claimed in claim 11 , wherein the processing circuitry is configured to determine whether the first bit is the information bit or the non-information bit by:
sorting Reed-Muller (RM) scores of N information bit indices in an ascending order, N being a length of a first codeword among the at least one codeword, and
dividing the N information bit indices into a plurality of subsets.
13. The device as claimed in claim 12 , wherein
the plurality of subsets comprises a first subset of indices, a second subset of indices, and a third subset of indices, the first subset of indices having an RM score less than a boundary RM score, the second subset of indices having an RM score greater than the boundary RM score, and the third subset of indices having an RM score equal to the boundary RM score; and
the processing circuitry is configured to:
allocate the first subset of indices to a frozen set,
allocate the second subset of indices to a set of information bit indices, and
select an action for the third subset of indices based on a current state among the plurality of states and a policy.
14. The device as claimed in claim 13 , wherein the processing circuitry is configured to:
update a value function of a current state action pair based on the selection of the at least one of the reward or the penalty; and
update a respective value function of all state action pairs taken during an episode based on termination of the episode or removal of all zero codewords among the plurality of codewords from a list.
15. The device as claimed in claim 9 , wherein the processing circuitry is configured to select one bit index in each iteration for which a corresponding PAC code achieves a minimum Hamming distance.
16. The device as claimed in claim 9 , wherein the processing circuitry is configured to select the at least one of the reward or the penalty including:
allocating the reward in response to determining that the first bit is correctly decoded, and
allocating a partial reward or a partial penalty based on a position of all zero codewords among the plurality of codewords in a list.
17. The method as claimed in claim 1 , further comprising:
generating, by the processing circuitry, a communication signal based on the at least one PAC code.
18. The method as claimed in claim 17 , further comprising:
transmitting, by the processing circuitry, the communication signal to at least one device via a communication channel.
19. The device as claimed in claim 9 , wherein the processing circuitry is configured to generate a communication signal based on the at least one PAC code.
20. The device as claimed in claim 19 , wherein the processing circuitry is configured to transmit the communication signal to at least one other device via a communication channel.