Granular gain of low-dimensional lattices based on binary linear codes is estimated using a quantization algorithm which is equivalently a soft-decision decoding of the underlying code. It is shown that substantial portion of the ultimate granular gain is achieved even in limited dimensions.

This letter treats lossy source coding of binary sources with short linear block codes. It is numerically shown that very simple basis-reprocessing approach yields good rate-distortion performance with manageable computational complexity for small block lengths. The result for code lengths up to 100 outperforms the message-passing based encoding for low-density codes which are several times longer.