Polar codes with partial repetition

An encoding apparatus for use in a communication channel, the encoding apparatus comprising:

• a transceiver;
• and
• a processor configured to:
• obtain a threshold for weights of rows in a polar coding generator matrix, wherein indices of the rows belong to an information set,
• obtain a smallest index of the information set with a weight less than or equal to the threshold,
• select a first candidate index based on a frozen index that is larger than the smallest index,
• select a second candidate index based on information indices that are smaller than a largest candidate frozen index and that corresponds to a weight less than or equal to the threshold,
• determine that a support of the first candidate index is distinct from a support of the second candidate index in at least two elements, and
• repeat, based on the determination, at least one bit from the second candidate index to the first candidate index.

A decoding apparatus for use in a communication channel, the decoding apparatus comprising:

• a transceiver configured to receive a polar code with partial repetition from the communication channel;
• and
• a processor configured to perform successive cancellation list decoding of the polar code with partial repetition, wherein the polar code with partial repetition is generated by:
• obtaining a threshold for weights of rows in a polar coding generator matrix, wherein indices of the rows belong to an information set,
• obtaining a smallest index of the information set with a weight less than or equal to the threshold,
• selecting a first candidate index based on a frozen index that is larger than the smallest index,
• selecting a second candidate index based on information indices that are smaller than a largest candidate frozen index and that corresponds to a weight less than or equal to the threshold,
• determining that a support of the first candidate index is distinct from a support of the second candidate index in at least two elements, and
• repeating, based on the determination, at least one bit from the second candidate index to the first candidate index.