## 6 Results and Discussion  
### Simulation Results  
The method to determine the parameters is finding the value with best BER performance at the same SNR. After simulations in MATLAB, we determined the values of \(T_{y}\), \(w\), \(W\), and \(T_{L}\) to be 4/10, 1, 5, and 4, respectively. The BER performance simulation of proposed low-complexity high-throughput QC-LDPC decoder architecture for proposed LDPC was carried out using BPSK modulation in an AWGN channel. Figure 10 illustrates the BER performance of our implementation. The six solid lines show the results of the MATLAB simulation. Three distinct decoding algorithms were employed, each executed over eight iterations, for both the CCSDS (8176, 7154) LDPC and the proposed LDPC code, yielding comprehensive simulation results. Initially, employing identical decoding algorithms, a minor coding gain loss of 0.5 dB was observed when applying the proposed LDPC in comparison to the original CCSDS (8176, 7154) LDPC code. This outcome underscores the effectiveness of our devised PCM, which yields a favorable performance comparable to the original CCSDS (8176, 7154) LDPC, and this 0.5 dB coding gain loss is acceptable considering that the throughput can be significantly improved by using the proposed LDPC with the same resource consumption. And, it can be found that no matter which PCM is used, there is a 1 dB coding gain loss using 2-bit MSA compared to MSA when the BER reaches \(10^{-6}\). This trade-off, albeit resulting in a BER performance compromise, remains acceptable, as the 2-bit MSA significantly reduces hardware resources and complexity, all while achieving approximately two-thirds reduction in resource overhead. Overall, our decoder simultaneously increases throughput and reduces decoding overhead by sacrificing BER performance. Meanwhile, we have selected four decoders with high throughput or low implementation complexity as the design principle and similar code rate, and compared the BER performance; the results are shown by four dashed lines in Figure 10. The decoder in [36] uses the (10368, 8448) LDPC from 5G NR with a code rate of 22/27, performs 10 iterations, employs 8-bit quantization, and the algorithm used is a layered decoding algorithm. It achieves a BER of \(10^{-6}\) at a Eb/N0 greater than 7. In comparison, this decoder has higher throughput and HUE, but obviously the coding gain for the same SNR is not as good as our decoder. The decoder in [37] uses the (2048, 1723) LDPC from IEEE 802.3 an with a code rate of about 7/8, five iterations, 4-bit quantization, and the decoding algorithm used is MSA. It has a SNR of 5.6 at a BER of \(10^{-6}\). This decoder has extremely high throughput, and its BER performance is slightly better than ours, but its fully parallel architecture leads to significant resource overhead. The decoder in [38] uses the constructed (4608, 4096) LDPC with a code rate of 8/9, performs six iterations, uses the decoding algorithm RR-BP proposed in that article, and the encoding and decoding process are both unquantized. Its BER achieves \(10^{-6}\) at a Eb/N0 of 6.7. There is no information about the implementation of this decoder, but it is clear that its BER performance lags behind our decoder by almost 2 dB. The decoder of [39] uses CCSDS (8176, 7154) LDPC with code rate 7/8, performing 20 iterations, the decoding algorithm used is NMS, and the encoding and decoding process are both unquantized. Its BER achieves \(10^{-6}\) a Eb/N0 of 3.9. The NMS used by this decoder has about 0.5 dB performance improvement compared to MSA, but due to our deep overlap structure, our decoder has much higher HUE and we have higher throughput with the same resource consumption. We designed the overlap decoder using 2 bit MSA, with low resource consumption and high throughput as the design criterion.