Analog codes on graphs

Many channels (e.g., the broadcast channels) require combined coding and modulation to approach capacity. Furthermore, it is often desirable to have a graceful degradation of information rate with decreasing SNR. In these situations, codes over large alphabets are advantageous. In this work, we consider analog codes, whose alphabet is the real line K. Traditionally, decoding analog codes has been difficult. Herein, we introduce capacity-approaching codes defined on graphs along with a novel superposition strategy that admits infinitely many resolutions. This superposition strategy makes it possible to derive an efficient iterative decoder for our analog codes, based on the sum-product algorithm. The resulting coding scheme performs close to the Shannon capacity of a band-limited AWGN channel, over a wide range of SNRs. Furthermore, we construct bandwidth efficient codes by truncating analog codes, and find that these perform well in comparison to MPSK cutoff rates.