Non-Binary Low Density Parity Check Codes for Satellite Communications

In this paper, we study a new class of Low Density Parity Check codes, designed for satellite communications, and achieving both high spectral efficiency and large coding gain. Given a constant-envelope 8-PSK constellation, a generic linear binary code does not lead to a geometrically uniform Euclidean-space code. Low Density Parity Check codes over Z_8, the group of integers modulo 8, are considered. When applied to 8-PSK, they generate geometrically uniform Euclidean space codes: distance profile and word error probability are the same for each transmitted codeword. These properties highly simplify both design and analysis. Some insights on code design, encoding, decoding, and simulated performance are provided.