In a decoder, a desired image is estimated by first retrieving coding modes from an encoded side information image. For each bitplane in the encoded side information image, syndrome bits or parity bits are decoded to obtain an estimated bitplane of quantized transform coefficients of the desired image. A quantization and a transform are applied to a prediction residual obtained using the coding modes, wherein the decoding uses the quantized transform coefficients of the encoded side information image, and is based on previously decoded bitplanes in a causal neighborhood. The estimated bitplanes of quantized transform coefficients of the desired image are combined to produce combined bitplanes. Then, an inverse quantization, an inverse transform and a prediction based on the coding modes are applied to the combined bitplanes to recover the estimate of the desired image.