We present a tandem scheme for Gaussian source compression, where a dead-zone quantizer is concatenated with a ternary low density generator matrix (LDGM) code. Both theoretical analysis and simulation results show that the LDGM codes can be universally optimal for near-lossless compression of ternary sources. Consequently, the distortion with the tandem scheme is mainly caused by the quantization, which can be negligible for high-rate quantizer. The most distinguished feature of the proposed scheme is its flexibility. The dead-zone quantizer can choose a suitable quantization level according to the distortion allowed, while the LDGM codes can adapt the code rate to approach the entropy of the quantized sequence. This is helpful to trade off between bandwith and distortion. In the meanwhile, the proposed scheme is robust when combined with the channel codes for transmission over noisy channels because of the fixed-length feature. Theoretically, we have proved that the block LDGM codes can achieve a lossless compression performance for ternary source in terms of the Hamming distortion, which is measured by the symbol error rate (SER). Practically, we develop a special class of LDGM codes, referred to as block Markov superposition transmission (BMST) of repetition codes, for compression of Gaussian sources. Numerical results show that: 1) the proposed scheme performs well for ternary sources over a wide range of code rates; 2) the distortion introduced by quantization dominates provided that the code rate is slightly greater than the discrete entropy.