Performance of NR LDPC Codes

Last updated on Mar 13, 2023

NR LDPC (New Radio Low-Density Parity-Check) codes are a type of error-correcting codes used in the 5G wireless communication standard. These codes have gained significant attention due to their excellent error-correcting capabilities, high flexibility, and low complexity. In this article, we will discuss the technical details of the performance of NR LDPC codes.

Introduction to NR LDPC Codes

NR LDPC codes are a class of linear error-correcting codes that use sparse parity check matrices. These codes have a low-density parity-check matrix, which means that most of the elements in the matrix are zero. The sparsity of the matrix results in a low complexity encoder and decoder implementation.

NR LDPC codes use two types of matrices: base matrices and expansion matrices. The base matrix is a fixed matrix used to generate the parity check matrix for different code rates and block lengths. The expansion matrix is a variable matrix used to generate different parity check matrices for the same base matrix.

The NR LDPC codes support a wide range of code rates and block lengths, making them highly flexible for different communication scenarios. The NR LDPC codes also have excellent error-correcting capabilities, which enable reliable communication in harsh wireless channels.

Performance Metrics of NR LDPC Codes

The performance of NR LDPC codes can be evaluated using several performance metrics, such as the bit error rate (BER), block error rate (BLER), coding gain, and throughput.

Bit Error Rate (BER)

The BER is the probability that a bit in the transmitted message is received incorrectly. The BER is a commonly used performance metric for digital communication systems, as it reflects the quality of the received signal.

In NR LDPC codes, the BER can be calculated as the ratio of the number of incorrectly decoded bits to the total number of transmitted bits. The BER depends on several factors, such as the channel quality, code rate, block length, and decoding algorithm.

Block Error Rate (BLER)

The BLER is the probability that the entire transmitted block of bits is received incorrectly. The BLER is a more stringent performance metric than the BER, as it reflects the probability of losing an entire block of information.

In NR LDPC codes, the BLER can be calculated as the ratio of the number of incorrectly decoded blocks to the total number of transmitted blocks. The BLER depends on several factors, such as the channel quality, code rate, block length, and decoding algorithm.

Coding Gain

The coding gain is the improvement in signal-to-noise ratio (SNR) achieved by the error-correcting code. The coding gain is a measure of the effectiveness of the code in reducing the effects of channel noise.

In NR LDPC codes, the coding gain can be calculated as the difference between the SNR required to achieve a certain BER with and without the error-correcting code. The coding gain depends on several factors, such as the channel quality, code rate, block length, and decoding algorithm.

Throughput

The throughput is the amount of information that can be transmitted per unit time. The throughput is an important performance metric for communication systems, as it reflects the efficiency of the system in transmitting information.

In NR LDPC codes, the throughput can be calculated as the product of the code rate and the channel capacity. The channel capacity is the maximum amount of information that can be transmitted over a noisy channel, and it depends on several factors, such as the channel quality and bandwidth.

Decoding Algorithms for NR LDPC Codes

The performance of NR LDPC codes depends on the decoding algorithm used to decode the received signal. The decoding algorithm is responsible for recovering the transmitted message from the noisy received signal.

There are several decoding algorithms available for NR LDPC codes, such as the belief propagation (BP) algorithm, the min-sum algorithm, the offset min-sum algorithm, and the layered min-sum algorithm. These algorithms have different complexities and trade-offs between performance and complexity.

The BP algorithm is a message-passing algorithm that iteratively updates the probability distributions of the transmitted bits based on the received signal and the parity check matrix. The BP algorithm has good error-correcting capabilities and can achieve near-optimal performance in low to moderate SNR regimes. However, the BP algorithm has a high complexity and requires a large amount of memory to store the probability distributions.

The min-sum algorithm is a simplified version of the BP algorithm that approximates the message updates using a minimum function. The min-sum algorithm has a lower complexity than the BP algorithm and requires less memory. However, the min-sum algorithm has a suboptimal performance compared to the BP algorithm, especially in high SNR regimes.

The offset min-sum algorithm is a modified version of the min-sum algorithm that introduces an offset parameter to balance the trade-off between performance and complexity. The offset min-sum algorithm can achieve a better performance than the min-sum algorithm while maintaining a lower complexity than the BP algorithm.

The layered min-sum algorithm is a variation of the min-sum algorithm that divides the parity check matrix into layers and performs message updates sequentially for each layer. The layered min-sum algorithm has a lower complexity than the BP algorithm and can achieve near-optimal performance in low to moderate SNR regimes.

Performance of NR LDPC Codes in 5G Systems

The NR LDPC codes are used in the physical layer of the 5G wireless communication standard to provide reliable communication in harsh wireless channels. The 5G NR LDPC codes support a wide range of code rates and block lengths, ranging from 1/5 to 5/6 and from 40 to 8424, respectively.

The performance of the NR LDPC codes in the 5G system depends on several factors, such as the channel quality, code rate, block length, and decoding algorithm. The 5G system uses a hybrid automatic repeat request (HARQ) mechanism to improve the performance of the NR LDPC codes by retransmitting the lost blocks.

The 5G system also uses a rate matching mechanism to adapt the code rate of the NR LDPC code to the transmission rate of the communication system. The rate matching mechanism involves puncturing and shortening the LDPC codeword to increase or decrease the code rate, respectively.

The performance of the NR LDPC codes in the 5G system has been extensively evaluated through simulations and experiments. The simulations and experiments have shown that the NR LDPC codes can achieve excellent error-correcting capabilities and high flexibility, making them suitable for different communication scenarios.

Conclusion

NR LDPC codes are a type of error-correcting codes used in the 5G wireless communication standard. These codes have a low-density parity-check matrix, which results in a low complexity encoder and decoder implementation. The NR LDPC codes support a wide range of code rates and block lengths, making them highly flexible for different communication scenarios.

The performance of the NR LDPC codes can be evaluated using several performance metrics, such as the bit error rate (BER), block error rate (BLER), coding gain, and throughput. The performance of the NR LDPC codes depends on several factors, such as the channel quality, code rate, block length, and decoding algorithm.

In summary, NR LDPC codes are a promising error-correcting code used in the 5G wireless communication standard. These codes have a low-density parity-check matrix, making them highly flexible and suitable for different communication scenarios. The performance of the NR LDPC codes can be evaluated using several performance metrics, and the decoding algorithm can be selected based on the trade-offs between performance and complexity. Overall, the NR LDPC codes offer excellent error-correcting capabilities and high flexibility, making them a valuable tool for reliable wireless communication in 5G systems.