  Recent work has suggested that low-density generator matrix (LDGM) codes are
likely to be effective for lossy source coding problems. We derive rigorous
upper bounds on the effective rate-distortion function of LDGM codes for the
binary symmetric source, showing that they quickly approach the rate-distortion
function as the degree increases. We also compare and contrast the standard
LDGM construction with a compound LDPC/LDGM construction introduced in our
previous work, which provably saturates the rate-distortion bound with finite
degrees. Moreover, this compound construction can be used to generate nested
codes that are simultaneously good as source and channel codes, and are hence
well-suited to source/channel coding with side information. The sparse and
high-girth graphical structure of our constructions render them well-suited to
message-passing encoding.
