Systems and methods for communicating using nested low density parity check codes
Systems and methods in accordance with various embodiments of the invention enable communicating using nested Low Density Parity Check (LDPC) codes. A nested LDPC code is an LDPC code having a full blocklength, where shorter blocklengths of the nested LDPC code can be utilized as shorter blocklength LDPC codes. In certain embodiments, a transmitter utilizes a nested LDPC code to communicate via a point-to-point connection. In several embodiments, multiple transmitters utilize nested LDPC codes to communicate simultaneously via a Random Access Channel. One embodiment includes a transmitter capable of encoding a message as symbols using a nested LDPC code until a feedback message indicating an end of epoch message is received. A receiver can determine whether a decoding rule is satisfied at predetermined decode times and transmit an end of epoch message when the decoder can decode a message based upon the nested LDPC code.
1. 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.
2. The communication system of claim 1 , wherein:
the full blocklength corresponds to a longest decode time from the set of predetermined decode times; and
each of the one or more shorter blocklength LDPC codes corresponds to a decode time from the set of predetermined decode times that is shorter than the longest decode time from the set of predetermined decode times.
3. The communication system of claim 1 , wherein:
the one or more shorter blocklength LDPC codes comprise a first shorter blocklength LDPC code and a second shorter blocklength LDPC code;
the first shorter blocklength LDPC code comprises a first set of variable nodes, and a first set of check nodes; and
the second shorter blocklength LDPC code comprises:
a second set of variable nodes comprising: the first set of variable nodes and an incremental set of variable nodes; and
a second set of check nodes comprising: the first set of check nodes, and an incremental set of check nodes.
4. The communication system of claim 3 , wherein:
the first set of check nodes are connected to one or more variable nodes from the first set of variable nodes; and
the incremental set of check nodes are connected to one or more variable nodes from the second set of variable nodes.
5. The communication system of claim 3 , wherein a ratio of the first set of variable nodes to the first set of check nodes is different from a ratio of the second set of variable nodes to the second set of check nodes.
6. The communication system of claim 1 , wherein determining whether a decoding rule is satisfied is based upon the received observed symbols.
7. The communication system of claim 1 , wherein the at least one encoder is configured to select a specific nested LDPC code based upon the start of epoch message.
8. The communication system of claim 1 , wherein:
the at least one encoder is a plurality of encoders; and
multiple encoders in the plurality of encoders are configured to select the same nested LDPC code to use when encoding the message data as symbols using the rateless code.
9. The communication system of claim 1 , wherein:
the at least one encoder is a plurality of encoders; and
at least two of the plurality of encoders are configured to select different nested LDPC codes to use when encoding the message data as symbols using the rateless code.
10. The communication system of claim 9 , wherein at least two of the different nested LDPC codes have different code rates.