LDPC code design considerations for non-uniform channels

Irregular low-density parity-check (LDPC) code design for parallel sub-channels with different qualities is investigated. Such channels appear in many communication systems, e.g., orthogonal frequency-division multiplexing systems. When channel knowledge is available at both the transmitter and receiver, following the literature, we consider allotted LDPC codes which carefully assign different parts of the code to sub-channels. To reduce the number of design parameters and allow for efficient design, semi-regular allotted codes have been suggested. We first formulate the design of semi-regular codes as a mixed integer linear programming. Relaxing the semi-regularity constraint broadens the search space which results in improved codes and also a more efficient design via linear programming. While information theoretic results suggest that having channel state information-for a fixed power assignment-does not change the capacity, we show that under non-optimal decoding or when the maximum degree allowed in the code is small, allotted codes significantly outperform conventional ones. Finally, for the case that neither side has the channel knowledge (thus capacity-loss is inevitable), we see that the reduced capacity can still be approached by LDPC codes.