Systems and methods for concurrent decoding of product lifted low density parity check (ldpc) codes

A method comprising:

• receiving, by a receiver, encoded data;
• identifying, by one or more processors, a low-density parity-check (LDPC) code corresponding to a bipartite graph comprising a set of edges connected between a first set of nodes and a second set of nodes, wherein the LDPC code is generated using a first LDPC code associated with a first subset of the second set of nodes and a second LDPC code associated with a second subset of the second set of nodes;
• generating, by the one or more processors, using the encoded data, a first set of messages and a second set of messages;
• communicating, by the one or more processors, using the bipartite graph, the first set of messages with the first subset and the second set of messages with the second subset, concurrently;
• and
• identifying, by the one or more processors, decoded data based at least on processing of the first set of messages and the second set of messages.

An apparatus comprising:

• a receiver configured to receive encoded data;
• and
• one or more processors are configured to:
• identify a low-density parity-check (LDPC) code corresponding to a bipartite graph comprising a first bipartite graph and a second bipartite graph, which share one or more edges, wherein the LDPC code is generated using a first LDPC code associated with the first bipartite graph and a second LDPC code associated with the second bipartite graph;
• generate, using the encoded data, a first set of messages and a second set of messages;
• communicate, using the first bipartite graph, the first set of messages and communicate, using the second bipartite graph, the second set of messages, concurrently;
• and
• identify decoded data based at least on processing of the first set of messages and the second set of messages.