LDPC Optimization For Multiple Access Channels

Multiple access channel is one of the most important issues in information theory. Ahlswede, Cover and Wyner have successively studied the problem of finding the capacity region of multiple access channels. However, they did not provide the method to approach it. The capacity of multiple access channels is limited by multi-user interference. Multi-access techniques, such as FDMA, TDMA and CDMA, are designed to handle this multi-user interference problem. For TDMA and FDMA, they solve the interference problem by employing orthogonal waveforms for different users. However, in information theory, it is proved that the communication system can achieve larger capacity by adopting non-orthogonal waveforms (such as CDMA) rather than adopting orthogonal waveforms (such as TDMA and FDMA) to distinguish between users. In recent years, Li Ping et al. proposed a new multi-user access technique which utilizes non-orthogonal waveforms by employing interleavers to distinguish signals between users, called Interleave-Division Multiple-Access (IDMA), and its improved performance and low receiver complexity make it an ideal technology for 4G systems.Low density parity check (LDPC) codes were rediscovered in the 1990s and have shown their ability to approach the Shannon limit on single user AWGN channel. Also, LDPC codes exhibit the threshold phenomenon: as the block size goes to infinite, an arbitrarily small bit-error-rate (BER) can be achieved when the noise level is lower than a certain threshold. Richardson and Urbanke developed the density evolution algorithm to determine the thresholds of the LDPC codes ensembles defined by their degree distributions in the single user case. Later, Chung, Richardson and Urbanke proposed the density evolution using a Gaussian approximation to estimate the performance of LDPC codes on single user AWGN channel based on the Gaussian characteristic of it, with the complexity greatly reduced and loss of accuracy negligible. However, when refer to the multiple access channels, the LDPC codes with notable performances on single user AWGN channel perform much worse while the threshold predicting methods mentioned above are not applicable for it.In this paper, we consider designing LDPC codes with powerful performance on multiple access channels. First, we proposed a novel detection algorithm with improved performances the decoding scheme for the LDPC-coded IDMA systems. Then a Gaussian approximation based density evolution algorithm is developed to analyze the iterative decoding process and predict the performances of the LDPC codes used in the IDMA systems. Also, when the system bandwidth efficiency is 1, by combining the differential evolution technology, the LDPC codes are optimized to find the optimal degree distributions of LDPC codes for IDMA systems under certain code rate and constant number of users. The simulation results show that the estimated thresholds are very close to the ones derived from simulations. It is also illustrated that the optimized LDPC codes perform much better than the regular (3, 6) LDPC codes, which perform well on single user AWGN channel, and the irregular LDPC codes optimized for single user AWGN channel.Then we extend our results to a more general situation. We proposed a multiuser communication system which employs the user-specific LDPC parity-check matrix as the unique characteristic of each user. We call this system as LDPCMA (LDPC multiple access) system.