## 4 Performance Evaluation and Result Analysis
### Performance Indicators  
The International Telecommunication Union--Radiocommunication Sector (ITU-R) has established several key performance indicators (KPIs) that are linked to 5G standards [46]. For coding schemes, decoders determine a communication system's compliance with ITU-R KPIs in mMTC, eMBB, and URLLC use cases. Processing latency, throughput, error correction, flexibility, area efficiency, and energy efficiency are the key decoding KPIs, which are discussed as follows:  
1. Error correction--The reliability of a communication system at the block level is determined by the BLER. The ratio of blocks received in error to the total blocks transmitted over a specified number of frames is known as the block error rate (BLER), which is a physical-layer error estimation technique. For mission-critical 6G URLLC applications, only one block out of every \(10^{9}\) should experience significant transmission faults that the channel decoder cannot fix, i.e., reliability on the order of \(10^{-9}\)[47].
2. Throughput--A crucial performance indicator of the decoder is the throughput, which is the number of bits that are successfully decoded per second. Since the channel decoder processes all received data, a high level of parallel processing is necessary to achieve a high throughput. The throughput of a fully parallel decoder where each bit is decoded in one clock cycle is given as \[T=f\times N\] (5) where \(f\) is the clock frequency and \(N\) is the block length. For an iterative decoder, the effective throughput is given as \[T=\frac{f\times P}{I}\] (6) where \(P\) is the number of bits per cycle and \(I\) is the number of iterations [48]. Throughput is expressed in bits per second (bps).
3. Latency--The URLLC applications of 6G have the most stringent latency requirements. Moreover, other physical-layer processes, including channel estimation and demodulation, take place in this latency limit with channel decoding. The time needed to process a received codeword and produce decoded bits of information is known as the decoder latency. A decoder's latency (L) in relation to throughput (T) and block length (N) can be expressed as \[L=N/T\] (7) where \(N\) is the block length in bits and \(T\) is the throughput in bits/second (bps); therefore, latency is expressed in seconds.
4. Computational complexity--URLLC requires low-complexity decoders in addition to efficient encoders. A typical way to quantify the computational complexity of decoding methods is to look at how many operations, such as comparisons, additions, multiplications, or bit manipulations, are needed in relation to the block length and code parameters. Computational complexity is generally expressed as the number of operations per bit or the number of operations per codeword [49].
5. Energy efficiency--It is estimated that the information and communications technology (ICT) sector is responsible for 5% of global carbon emissions. Energy consumption in the 5G domain, measured in bits/joule, has been seen as a crucial design parameter due to global energy-efficiency initiatives. The energy efficiency (EE) of a decoder in acommunication system is expressed as the ratio of data transmission rate (throughput) to consumed power [50], and is expressed as \[EE=T/P_{c}\] (8) where \(T\) is the throughput and \(P_{c}\) is the consumed circuit power. The unit of EE is bits/joule.
6. Area efficiency--The area efficiency (AE) of a decoder is expressed as \[AE=T/A\] (9) where \(T\) is the information throughput and \(A\) is the chip area. The unit of \(AE\) is (Mbps/mm\({}^{2}\)) or (Gbps/mm\({}^{2}\)) [48].