Repeat-Accumulate Signal Codes

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.