Method and apparatus for wirelessly communicating over a noisy channel with a variable codeword length polar code to improve transmission capacity

A method comprising:

• encoding an input vector with an original polar code encoder to produce an initial codeword, wherein the original polar code encoder is an asymmetric polar code encoder for an asymmetric polar encoded codeword;
• transmitting the initial codeword to a receiving device;
• receiving, from the receiving device, feedback from which it can be concluded that the initial codeword was not decoded successfully;
• after the receiving the feedback, generating an extended input vector by extending the input vector to include an extension vector that comprises at least one redundancy bit;
• after the generating, encoding the extended input vector with an additional asymmetric polar code encoder based on a combination of the original polar code encoder, a further polar code encoder having a size equal to the size of the extension vector, and a further polarizing stage that links outputs of the original polar code encoder and the further polar code encoder;
• and
• transmitting an output of the further polarizing stage.

An apparatus comprising:

• an input interface that obtains an input bit sequence containing N1+N2 bits including information bits and frozen bits, where N1 and N2 are different powers of a polar code kernel size;
• a first polar code encoder that polar encodes N1 bits of the input bit sequence with a first constituent polar encoder to produce a first set of N1 polar encoded bits;
• a second polar code encoder that polar encodes N2 bits of the input bit sequence with a second constituent polar encoder, to produce a second set of N2 polar encoded bits;
• a first additional polarizing stage that combines at least some of the first set of N1 polar encoded bits with at least some of the second set of N2 polar encoded bits to produce a set of N1 combined bits after the first set of N1 polar encoded bits and the second set of N2 polar encoded bits are produced;
• a codeword generator that generates an asymmetric polar encoded codeword of length N1+N2 consisting of the set of N1 combined bits and the N2 polar encoded bits;
• and
• a transmitter that transmits the asymmetric polar encoded codeword over a wireless channel.

An apparatus comprising:

• an original polar code encoder that encodes an input vector to produce an initial codeword, wherein the original polar code encoder is an asymmetric polar code encoder for an asymmetric polar encoded codeword;
• a transmitter that transmits the initial codeword to a receiving device;
• a receiver that receives feedback from the receiving device from which it can be concluded that the initial codeword was not decoded successfully;
• an extended input vector generator that generates an extended input vector by extending the input vector to include an extension vector that comprises at least one redundancy bit after the feedback is received;
• and
• an additional asymmetric polar code encoder that encodes the extended input vector after the extended input vector is generated, wherein the additional asymmetric polar code encoder is based on a combination of the original polar code encoder, a further polar code encoder having a size equal to the size of the extension vector, and a further polarizing stage that links outputs of the original polar code encoder and the further polar code encoder,
• wherein the transmitter further transmits an output of the further polarizing stage.

An apparatus comprising:

• at least one processor operatively coupled to a memory and a transceiver, the at least one processor configured to:
• obtain an input bit sequence containing N1+N2 bits, the input bit sequence including information bits and frozen bits, where N1 and N2 are different powers of a polar code kernel size;
• polar encode N1 bits of the input bit sequence with a first constituent polar encoder to produce a first set of N1 polar encoded bits;
• polar encode N2 bits of the input bit sequence with a second constituent polar encoder to produce a second set of N2 polar encoded bits;
• after the first set of N1 polar encoded bits and the second set of N2 polar encoded bits are produced, combine at least some of the N1 polar encoded bits with at least some of the N2 polar encoded bits with a first additional polarizing stage to produce a set of N1 combined bits;
• and
• generate an asymmetric polar encoded codeword of length N1+N2 consisting of the set of N1 combined bits and the N2 polar encoded bits.

A non-transitory computer-readable medium having instructions stored thereon that, when executed by an apparatus, cause the apparatus to perform operations, the operations comprising:

• obtaining an input bit sequence containing N1+N2 bits, the input bit sequence including information bits and frozen bits, where N1 and N2 are different powers of a polar code kernel size;
• polar encoding N1 bits of the input bit sequence with a first constituent polar encoder to produce a first set of N1 polar encoded bits;
• polar encoding N2 bits of the input bit sequence with a second constituent polar encoder to produce a second set of N2 polar encoded bits;
• after the encoding the N1 bits and the encoding the N2 bits, combining at least some of the first set of N1 polar encoded bits with at least some of the second set of N2 polar encoded bits with a first additional polarizing stage to produce a set of N1 combined bits;
• and
• generating an asymmetric polar encoded codeword of length N1+N2 consisting of the set of N1 combined bits and the second set of N2 polar encoded bits.