  This paper proposes the Symbolic-Stochastic Chase Decoding Algorithm (S-SCA)
for the Reed-Solomon (RS) and BCH codes. By efficient usage of void space
between constellation points for $q$-ary modulations and using soft information
at the input of the decoder, the S-SCA is capable of outperforming conventional
Symbolic-Chase algorithm (S-CA) with less computational cost. Since the S-SCA
starts with the randomized generation of likely test-vectors, it reduces the
complexity to polynomial order and also it does not need to find the least
reliable symbols to generate test-vectors. Our simulation results show that by
increasing the number of test-vectors, the performance of the algorithm can
approach the ML bound. The S-SCA($1K$) provides near $2$ dB gain in comparison
with S-CA($1K$) for $(31, 25)$ RS code using $32$-QAM. Furthermore, the
algorithm provides near $3$ dB further gain with $1K$ iteration compared with
S-CA($65K$) when $(255, 239)$ RS code is used in an AWGN channel. For the
Rayleigh fading channel and the same code, the algorithm provides more that $5$
dB gain. Also for $(63, 57)$ BCH codes and $8$-PSK modulation the proposed
algorithm provides $3$dB gain with less complexity.
  This decoder is Soft-Input Soft-Output (SISO) decoder and is highly
attractive in low power applications. Finally, the Symbolic-Search
Bitwise-Transmission Stochastic Chase Algorithm (SSBT-SCA) was introduced for
RS codes over BPSK transmission that is capable of generating symbolic
test-vectors that reduce complexity and mitigate burst errors.
