Methods and apparatus for compactly describing lifted low-density parity-check (LDPC) codes

An apparatus for wireless communications, comprising:

• a memory;
• and
• at least one processor coupled with the memory and configured to:
• determine a first set of cyclic lifting values associated with a set of lifting size values and a base parity check matrix (PCM) associated with a base graph;
• select a lifting size value from the set of lifting size values;
• determine a second set of cyclic lifting values by computing a modulo of each of the first set of cyclic lifting values with respect to the selected lifting size value;
• determine a lifted PCM for generating a lifted low density parity check (LDPC) code by applying the second set of cyclic lifting values to interconnect edges in copies of the base graph;
• and
• at least one of:
• (i) encode a set of information bits, using the lifted LDPC code, to produce a set of encoded information bits and transmit the set of encoded information bits;
• or
• (ii) receive a set of encoded information bits and decode the set of encoded information bits, using the lifted LDPC code, to obtain a set of information bits.

An apparatus for wireless communications, comprising:

• means for determining a first set of cyclic lifting values associated with a set of lifting size values and a base parity check matrix (PCM) associated with a base graph;
• means for selecting a lifting size value from the set of lifting size values;
• means for determining a second set of cyclic lifting values by computing a modulo of each of the first set of cyclic lifting values with respect to the selected lifting size value;
• means for determining a lifted PCM for generating a lifted low density parity check (LDPC) code by applying the second set of cyclic lifting values to interconnect edges in copies of the base graph;
• and
• means for at least one of:
• (i) encoding a set of information bits, using the lifted LDPC code, to produce a set of encoded information bits and transmitting the set of encoded information bits;
• or
• (ii) receiving a set of encoded information bits and decoding the set of encoded information bits, using the lifted LDPC code, to obtain a set of information bits.

A non-transitory computer readable medium storing computer executable code thereon for wireless communications, comprising:

• code for determining a first set of cyclic lifting values associated with a set of lifting size values and a base parity check matrix (PCM) associated with a base graph;
• code for selecting a lifting size value from the set of lifting size values;
• code for determining a second set of cyclic lifting values by computing a modulo of each of the first set of cyclic lifting values with respect to the selected lifting size value;
• code for determining a lifted PCM for generating a lifted low density parity check (LDPC) code by applying the second set of cyclic lifting values to interconnect edges in copies of the base graph;
• and
• code for at least one of:
• (i) encoding a set of information bits, using the lifted LDPC code, to produce a set of encoded information bits and transmitting the set of encoded information bits;
• or
• (ii) receiving a set of encoded information bits and decoding the set of encoded information bits, using the lifted LDPC code, to obtain a set of information bits.