  A recent line of work has focused on the use of low-density generator matrix
(LDGM) codes for lossy source coding. In this paper, wedevelop a generic
technique for deriving lower bounds on the rate-distortion functions of binary
linear codes, with particular interest on the effect of bounded degrees. The
underlying ideas can be viewing as the source coding analog of the classical
result of Gallager, providing bounds for channel coding over the binary
symmetric channel using bounded degree LDPC codes. We illustrate this method
for different random ensembles of LDGM codes, including the check-regular
ensemble and bit-check-regular ensembles, by deriving explicit lower bounds on
their rate-distortion performance as a function of the degrees.
