## 4 Comparative Analysis Convolutional Codes with LDPC Codes, BCH Codes, and Turbo Codes  
The Viterbi decoding algorithm is designed to mitigate the errors caused by these signal distortions. It works by estimating the most likely data sequence that the satellite transmitted based on the observed received signal and the knowledge of the encoder. This  
Figure 8: Received codeword with two adjacent errors.  
involves searching a large number of possible data sequences and selecting the one that has the highest likelihood of being the transmitted data.  
In the case of multipath fading, the Viterbi decoding algorithm can track and compensate for the different signal delays and interference levels caused by the multiple signal paths. By comparing the decoded data sequence with the original data sequence, it can also detect and correct any errors that may have occurred due to signal distortions.  
There are other types of codes that are used in satellite communications in addition to Convolutional codes [18; 19], such as LDPC codes, BCH codes, and Turbo codes.  
The question is as follows: why can we not use one of these codes instead of the Convolutional Code and Viterbi algorithm in GPS Systems?  
Satellite communication systems often face challenges such as limited bandwidth, noise, and interference [20]. Convolutional codes and the Viterbi algorithm are well-suited to address these challenges, and their use in GPS communication systems is based on several requirements [21]:  
* **High data rate:** Satellite communication systems typically need to transmit high volumes of data over long distances. Convolutional codes are efficient error-correcting codes that can operate at high data rates. They can be implemented in hardware or software and enable the reliable transmission of large amounts of data.
* **Channel characteristics:** Satellite communication channels often suffer from fading and interference, which can cause errors and the degradation of the transmitted signal. Convolutional codes and the Viterbi algorithm are designed to deal with such channel impairments. Convolutional codes are powerful because their encoding and decoding processes involve comparing the received signal with the expected signal. The Viterbi algorithm can estimate the most likely transmission sequence from a received signal in spite of channel distortions.
* **Low computational complexity:** Satellite communication systems often have limited computational resources due to power and size constraints. Convolutional codes and the Viterbi algorithm are computationally efficient and require relatively few resources, making them suitable for use in satellite communication systems.
* **Real-time processing:** Satellite signals must be processed in real-time to provide real-time communication services. The algorithm used for the decoding needs to be fast and efficient, which is another reason why the Viterbi algorithm is often used. The algorithm has been proven to decode signals in real-time, making it a good fit for satellite communication systems.
* **Compatibility with modulation schemes:** Convolutional codes can be used with a variety of modulation schemes, including phase-shift keying (PSK) and quadrature amplitude modulation (QAM). This makes them a versatile choice for satellite communication systems, where different modulation schemes may be used depending on the specific requirements of the system.  
Based on the requirements of high data rate, channel characteristics, low computational complexity, real-time processing, and compatibility with modulation schemes, Convolutional codes with the Viterbi algorithm are well-suited for use in GPS systems.