Repeat-Accumulate Signal Codes

We propose a new state-constrained signal code, namely repeat-accumulate signal code (RASC). The original state-constrained signal code directly encodes modulation signals by signal processing filters, the filter coefficients of which are constrained over Eisenstein rings. Although the performance of signal codes is defined by signal filters, optimum filters were found by brute-force search in terms of symbol error rate (SER) in the literature because the asymptotic behavior with different filters has not been investigated. We introduce Monte Carlo density evolution (MC-DE) to analyze the asymptotic behavior of RASCs. Based on our analysis by MC-DE, the optimum filters can be efficiently found for given parameters of the encoder. Numerical results show the difference between the noise threshold and the Shannon limit is within 0.8 dB. We also introduce a low-complexity decoding algorithm. BCJR and fast Fourier transform-based belief propagation (FFT-BP) increase exponentially as the number of output constellations increase. The extended min-sum (EMS) decoder under constraint over Eisenstein rings is established to overcome this problem. Simulation results show the EMS decoder can reduce the computational complexity to less than 25% of that of BCJR and FFT-BP without a significant performance loss, which would be greater than approximately 1 dB.