Nested convolutional/turbo codes for the binary Wyner-Ziv problem

We show how concatenated (convolutional) codes can be used to compress close to the Wyner-Ziv limit for binary sources. Focusing on the case of lossy compression of an equiprobable memoryless binary source with side information at the decoder, the approach is based on nested binary linear codes, which is the extension of Wyner's lossless compression scheme to the lossy case proposed by Shamai, Verdu and Zamir. Based on our previous work on lossless compression with concatenated codes, we are able to combine the only two previously suggested nested schemes into a novel turbo scheme with improved performance. Our scheme can come within 0.09 bits from the theoretical limit, which to our knowledge is the first result ever reported for the binary Wyner-Ziv problem.