  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 symbol error rate because the asymptotic behavior with
different filters has not been investigated. Moreover, computational complexity
of the conventional BCJR used in the decoder increases exponentially as the
number of output constellations increase. 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 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 noise thresholds of RASC and
the Shannon limit is within 0.8 dB. 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.
