Advanced coding techniques and applications to CDMA

In this work, we propose low-complexity coding/decoding schemes to approach the capacity of binary-input symmetric-output channels and code division multiple access channels. In the first part of this thesis, we consider systematic random-like irregular repeat accumulate code ensembles of infinite block length, assuming transmission over a binary-input symmetric-output channel. The code ensemble is described by a Tanner graph, and is decoded by the message-passing belief propagation algorithm. Density evolution describes the evolution of message distributions that are passed on the Tanner graph of the code ensemble. Applying density evolution under the belief propagation decoder results in a dynamic system on the set of symmetric distributions. We formulate a general framework to approximate the exact density evolution with a one-dimensional dynamic system on the ensemble of real numbers. Based on this general framework, we propose four low-complexity methods to design irregular repeat accumulate code ensembles. These optimization methods are based on Gaussian approximation, reciprocal (dual) channel approximation and extrinsic mutual information transfer function, among other recently-developed tools. These methods allow us to design irregular repeat accumulate codes, of various rates, with vanishing bit error rate guaranteed by a local stability condition of the fixed-point of the exact density evolution recursions. Using the exact density evolution, the thresholds of the designed codes are evaluated, and are found to be very close to the Shannon limits of the binary input additive white Gaussian noise channel and the binary symmetric channel. For the binary-input additive white Gaussian noise channel, we investigate the performance of finite length irregular repeat accumulate codes, whose graph is conditioned so that either the girth or the minimum stopping set size is maximized. We compare the performances of the resulting IRA codes to those of random ensembles under maximum likelihood decoding, and to the performances of the best low density parity check codes of comparable graph conditioning. In the second part of this thesis, we develop a low-complexity coding/decoding scheme, to approach the capacity of random-spreading code division multiple access channels with Gaussian noise, in the large system limit. Our approach is based on the use of quaternary phase shift keying modulation, capacity-achieving binary error-correcting codes, linear minimum mean square error filtering and successive decoding. We optimize the power profile (respectively rate profile) in the case of equal-rate (respectively equal-power) users. In the equal-rate setting, it is found that the achievable spectral efficiency, when using low-rate binary error correcting codes, is very close to the optimum. Through simulations, we show that the system optimization carried out in the large-system limit and for infinite block length can be used to dimension finite-size practical systems with no error propagation throughout the successive decoding.