Code designs for nonuniform sources

A user equipment (UE), comprising:

• one or more memories storing processor-executable code;
• and
• one or more processors coupled with the one or more memories and individually or collectively operable to execute the code to cause the UE to:
• generate an encoding matrix comprising a set of information columns comprising systematic bits, a first set of core parity columns comprising a first set of parity bits, and one or more sets of extension parity columns comprising a second set of parity bits;
• puncture one or more of the systematic bits with the first set of parity bits, the second set of parity bits, or a combination thereof, based at least in part on an offset value indicating an initial column of the encoding matrix;
• and
• encode an initial message in accordance with the encoding matrix based at least in part on the offset value indicating the initial column of the encoding matrix.