Systems and methods for communicating using nested low density parity check codes

A communication system, comprising:

• at least one encoder configured to:
• receive a start of epoch message;
• encode message data as symbols using a rateless code determined using a nested Low Density Parity Check (LDPC) code by mapping a codeword to a symbol, wherein the nested LDPC code:
• is an LDPC code with a full blocklength;
• and
• comprises one or more shorter blocklength LDPC codes;
• and
• receive feedback messages at a predetermined set of potential decoding times, wherein the at least one encoder is configured to transmit symbols until a received feedback message is an end of epoch message;
• and
• a decoder, where the decoder is configured to:
• cause a broadcast transmitter to transmit at least one start of epoch message;
• receive observed symbols;
• at each of a set of predetermined decode times, determine whether a decoding rule is satisfied;
• and
• when the decoding rule is satisfied:
• decode at least one message based upon the received observed symbols based upon the nested LDPC code;
• and
• cause the broadcast transmitter to transmit an end of epoch message.