On the Error-Reducing Properties of Superposition Codes

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).