LDPC codes over rings for PSK modulation

This paper describes the design and analysis of low-density parity-check (LDPC) codes over rings and shows how these codes, when mapped onto appropriate signal constellations, can be used to effect bandwidth-efficient modulation. Specifically, LDPC codes are constructed over the integer rings /spl Zopf//sub m/ and G/sub m//sup 2/ and mapped onto phase-shift keying (PSK)-type signal sets to yield geometrically uniform signal space codes. This paper identifies and addresses the design issues that affect code performance. Examples of codes over /spl Zopf//sub 8/ and G/sub 64/ mapped onto 8-ary and 64-ary signal sets at a spectral efficiency of 1.5 and 2.0 bits per second per hertz (b/s/Hz) illustrate the approach; simulation of these codes over the additive white Gaussian noise (AWGN) channel demonstrates that this approach is a good alternative to bandwidth-efficient techniques based on binary LDPC codes-e.g., bit-interleaved coded modulation.