  Next-generation wireless communication systems impose much stricter
requirements for transmission rate, latency, and reliability. The peak data
rate of 6G networks should be no less than 1 Tb/s, which is comparable to
existing long-haul optical transport networks. It is believed that using long
error-correcting codes (ECC) with soft-decision decoding (SDD) is not feasible
in this case due to the resulting high power consumption. On the other hand,
ECC with hard-decision decoding (HDD) suffers from significant performance
degradation. In this paper, we consider a concatenated solution consisting of
an outer long HDD code and an inner short SDD code. The latter code is a
crucial component of the system and the focus of our research. Due to its short
length, the code cannot correct all errors, but it is designed to minimize the
number of errors. Such codes are known as error-reducing codes. We investigate
the error-reducing properties of superposition codes. Initially, we explore
sparse regression codes (SPARCs) with Gaussian signals. This approach
outperforms error-reducing binary LDPC codes optimized by Barakatain, et al.
(2018) in terms of performance but faces limitations in practical applicability
due to high implementation complexity. Subsequently, we propose an LDPC-based
superposition code scheme with low-complexity soft successive interference
cancellation (SIC) decoding. This scheme demonstrates comparable performance to
SPARCs while maintaining manageable complexity. Numerical results were obtained
for inner codes with an overhead (OH) of 8.24% within a concatenated scheme
(15% OH) with an outer hard-decision decoded staircase code (6.25% OH).
