Methods, systems, and apparatus for rateless polar coding and incremental redundancy

A method comprising:

• receiving a first reduced number of encoded bits and a second reduced number of encoded bits encoded by a polar code,
• the second reduced number of encoded bits comprising one or more of the encoded bits not included in the first reduced number of encoded bits and starting from a second starting position different from a first starting position of the first reduced number of the encoded bits,
• the polar code comprising a plurality of bit indices for placing bit values before encoding, the plurality of bit indices comprising:
• a first set of bit indices for placing values of input bits and a second set of bit indices for placing a predetermined bit value;
• and
• decoding the first reduced number of encoded bits and the second reduced number of encoded bits to obtain decoded input bits.

An apparatus comprising:

• an encoder configured to encode input bits by a polar code to obtain a number of encoded bits, the polar code comprising a plurality of bit indices for placing bit values before encoding, the bit indices comprising:
• a first set of bit indices for placing values of the input bits and a second set of bit indices for placing a predetermined bit value;
• and
• an interface coupled to the encoder, configured to:
• output a first reduced number of encoded bits starting from a first starting position;
• and
• output a second reduced number of encoded bits, the second reduced number of encoded bits comprising one or more of the encoded bits not included in the first reduced number of encoded bits and starting from a second starting position different from the first starting position.

An apparatus comprising:

• an interface configured to receive a first reduced number of encoded bits and a second reduced number of encoded bits encoded by a polar code,
• the second reduced number of encoded bits comprising one or more of the encoded bits not included in the first reduced number of encoded bits and starting from a second starting position different from a first starting position of the first reduced number of the encoded bits,
• the polar code comprising a plurality of bit indices for placing bit values before encoding, the plurality of bit indices comprising:
• a first set of bit indices for placing values of input bits and a second set of bit indices for placing a predetermined bit value;
• and
• the apparatus further comprising:
• a decoder, coupled to the interface, configured to decode the first reduced number of encoded bits and the second reduced number of encoded bits to obtain decoded input bits.