We investigate methods for power and bandwidth efcient communication. The approach we consider is based on powerful binary error correcting codes and we construct coded modulation schemes which are able to perform close to the capacity of the channel. We focus on the additive white Gaussian noise channel. For this channel a Gaussian distribution maximizes mutual information and signal shaping has to be used to get close to capacity. We investigate a simple method of signal shaping based on the superposition of binary random variables. With multistage decoding at the receiver, the original coding problem is transformed into a coding problem for a set of equivalent binary-input output-symmetric channels. It is shown that with the method signal constellations can be designed for high spectral efciencies which have their capacity limit within 0.1 dB of the capacity of the AWGN channel. Furthermore, low-density parity-check codes are designed for the equivalent binary channels resulting from this modulation method. We show how to approach the constrained capacity limit of the signal constellations we design very closely. A downside of multistage decoding is that multiple binary error-correcting codes are used. We show how one can limit the number of error-correcting codes used by merging bit-interleaved coded modulation and signal shaping. This results in a coded modulation scheme which is able to approach the capacity of the AWGN channel closely for any spectral efciency. These coded modulation methods transform the coding problem for the original channel into a coding problem for a set of binary channels. Depending on the design of the modulation scheme these channels are symmetric or not. We show how to characterize channel symmetry in general and how these results can be used to design coded modulation schemes resulting in a set of symmetric binary channels.
- coded modulation schemes
- gaussian noise channel
- bandwidth efficient communication