## 4 Performance Evaluation and Result Analysis
### Graphical Analysis  
This sub-section is the graphical analysis of the results from summary Tables 3 and 4. It includes Figures 3-6 for performance evaluation. With reference to Table 3, Figure 3 compares the required \(E_{b}/N_{0}\) (SNR) values of different decoders to attain a BLER of \(10^{-4}\) for the given values of the code lengths and code rates of the coding scheme. Analyzing the data from Table 4, Figure 4 gives the coding gain of different decoders in comparison with CA-SCL decoding of 5G NR polar code. Figure 5 gives the BLER performance of (128, 103) random linear code (RLC) under GRAND, AED, and OSD. It is evident that as the SNR increases, the error-correction performance of the decoder increases. For a target BLER of \(10^{-4}\), GRAND has superior performance. Comparative analysis is done by providing MATLAB plots for Figures 3 and 4. For Figure 5, Monte Carlo simulation is done for respective decoding techniques. For short codewords, the SNR requirement of URLLC applications is in the range of 10-20 dB. 1. For URLLC applications, short-block-length codes, which are preferred for low latency, generally have a lower reliability, often requiring a higher SNR to achieve the same error-correction performance as compared to long-block-length codes. Thus, in a finite-block-length regime, there exists a trade-off between the required SNR and code block length to achieve a target BER/BLER. The scatter plot in Figure 3 compares the SNR required to achieve a target BLER of \(10^{-4}\) for the decoding schemes. The data are collected from the performance analysis study of the decoders in the given reference articles, as listed in Table 3. The parameters of the coding scheme for which the decoding scheme attains the specific error rate are given in column three. The X-axis of the scatter plot has code block lengths ranging from 50 to 500. The Y-axis of the scatter plot gives the SNR range. Since the values of the SNR for achieving the target BLER have a wide range, the limits are set at 0-30 (dB). A lower SNR value for a short codewords is preferable for 6G URLLC and mMTC applications. By analyzing the plot, we can see that SCL-GRAND, adaptive-ordered statistics decoding (A-OSD), GRANDAB, and improved belief propagation list (IBPL) decoding are particularly scalable for URLLC use cases as the target BLER is achieved for shorter code lengths at lower SNR values for these decoding schemes. Figure 5: BLER vs. SNR for RLC (128, 103) and RLC (128, 64), applying GRAND, AED and OSD decoding schemes. Figure 6: Three-dimensional scatter plot for energy efficiency in relation to throughput and latency. 2. Coding gain is the reduction in signal-to-noise ratio (SNR) required to achieve a specific bit error rate (BER) or block error rate (BLER) when one coding scheme is compared with another. In other words, coding gain gives a measure of the energy efficiency of one coding scheme over another. 3 GPP and IEEE standards consider coding gain a key performance metric to select candidate codes. The bar graph of Figure 4 gives the coding gain of the referenced decoding schemes listed in Table 4, compared to the standardized SCL decoder for CA-Polar codes with specified parameters mentioned in column two of the table. The data are collected and analyzed from the error rate performance plots of the compared schemes, as provided in the referenced articles. The coding gain values are provided at different error rate thresholds and, hence, are an approximate evaluation. The X-axis represents the decoders, and the Y-axis represents the coding gain (in dB) that each decoder on the X-axis achieves over the reference decoding scheme mentioned in the legend. The plotted range reflects the values in our analysis, and the Y-axis scale is adjusted accordingly. It is observed that GRAND variants achieve a higher coding gain in comparison with other decoders over the SCL decoder for polar code.