We describe a data hiding technique which uses noise resilient channel codes based on multidimensional lattices. A trade-off between the quantity of hidden data and the quality of the watermarked image is achieved by varying the number of quantization levels for the signature and a scale factor for data embedding. Experimental results show that the watermarked image is transparent to embedding for large amount of hidden data, and the quality of the extracted signature is high even when the watermarked image is subjected to up to 75% Wavelet compression and 85% JPEG lossy compression. These results can be combined with a private key-based scheme to make unauthorized retrieval practically impossible, even with the knowledge of the algorithm.