State-constrained signal codes directly encode modulation signals using signal processing filters, the coefficients of which are constrained over the rings of formal power series. Although the performance of signal codes is defined by these signal filters, optimal filters must be found by brute-force search in terms of the symbol error rate because the asymptotic behavior with different filters has not been investigated. Moreover, the computational complexity of the conventional BCJR used in the decoder increases exponentially, as the number of output constellations increases. We hence propose a new class of state-constrained signal codes called repeat-accumulate signal codes (RASCs). To analyze the asymptotic behavior of these codes, we employ Monte Carlo density evolution (MC-DE). As a result, the optimum filters can be efficiently found for the given parameters of the encoder. We also introduce a low-complexity decoding algorithm for RASCs called the extended min-sum (EMS) decoder. The MC-DE analysis shows that the difference between the noise thresholds of RASC and the Shannon limit is within 0.8 dB. The simulation results moreover show that the EMS decoder can reduce the computational complexity to less than 25% of that of conventional decoder without degrading the performance by more than 1 dB.

In this paper, we focus on a X channel; a system with two transmitters and two receivers each equipped with a single antenna, where independent messages need to be conveyed over channels from each transmitter to each receiver. A key concept of that arises in the context of the X channel is interference alignment (IA) that refers to an overlap of signal spaces occupied by undesired interference at each receiver while keeping desired signal spaces distinct. However, all the channel responses and the precise time synchronization are required at every transmitter and receiver to realize the IA, which are seriously demanding in practice. In this paper, we propose semi-blind IA (S-BIA) scheme exploiting frequency selectivity of wireless channels using orthogonal frequency division multiplexing (OFDM), which only requires channel responses corresponding to each transmitter. Numerical results confirm that proposed S-BIA can achieve the same degrees of freedom as conventional IA even in the presence of time synchronization errors.