## 3 Candidate Generation in Parallel Decoding of Rate-1 Nodes
### Candidate Generation Based on Partially Ordered Candidate Sets
We described a partial order for the PMs of all possible candidates and used it to propose an algorithm for the generation of these required candidates. The presented upper bound for the number of candidates is significantly smaller than the state-of-the-art upper bound. For practical decoder implementations, we introduced an extended threshold for the candidate selection, which reduces the number of paths by up to 53.1%. The resulting ExPOS-Fast-SSCL decoding exhibits a minor error-correction performance degradation, which can be tuned in trade-off with the candidate reduction. Unrolled decoder hardware implementations for high throughput benefit from these reductions, which was shown by a set of decoder implementations for \(N=128\) and \(L\in\{2,4,8\}\) in a 28 nm FD-SOI CMOS technology. The highest improvements of 158.8% regarding the area efficiency and 62.5% in terms of energy efficiency were observed for \(L=8\) within the set of the presented implementations. The presented algorithms and the corresponding architectures of Rate-1 nodes enable unrolled high-throughput decoder architectures with list sizes \(L>2\) to approach reasonable implementation costs. In future research, the proposed algorithm may be applied to other node types besides Rate-1 nodes, in order to further improve Fast-SSCL decoder implementations. Moreover, the results may also be combined with other complexity reduction mechanisms or be used in other decoder architectures like partially unrolled decoders for different target platforms, e.g., Field Programmable Gate Arrays (FPGAs). Conceptualization, L.J., C.K., O.G., T.V. and N.W. ; methodology, L.J. ; software, L.J., C.K. and O.G. ; validation, L.J., C.K. and O.G. ; formal analysis, L.J., C.K. and O.G. ; investigation, L.J. ; resources, L.J. ; data curation, L.J. ; writing--original draft preparation, L.J., C.K., O.G., T.V. and N.W. ; visualization, L.J. ; supervision, T.V. and N.W. ; project administration, T.V. and N.W. All authors have read and agreed to the published version of the manuscript. This work was funded in part by the German Federal Ministry for Economic Affairs and Energy (BMWi) under grant ZF4013407 PR7 and the German Federal Ministry of Education and Research (BMBF) under grant 16 KIS185 (FunKI). The data presented in this study are available on request from the corresponding author. The authors would like to thank [PERSON] and [PERSON], Creonic GmbH, 67655 Kaiserslautern, for helpful discussions on the relations between PMs, on which the presented findings in Section 3.1 are based. The authors declare no conflict of interest. ## References

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