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 R 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.