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Tikrit Journal of Engineering Sciences

Performance Analysis of Different Flexible Decoding Algorithms for NR-LDPC Codes

Layla Mahdi Salih, Thuraya Mahmood Qaradaghi, Jalal J. Hamad Ameen

Published Dec 11, 2022• 3 citations

Abstract

Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.

DOI: 10.25130/tjes.29.4.2

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Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.

The development of the Fifth Generation (5G) New Radio (NR) provides several significant advantages when compared to the fourth generation (4G) Long Term Evolution (LTE) in mobile communications. Due to the outstanding characteristics of Low-Density Parity-Check (LDPC) codes such as high decoding performance, high throughput, low complexity, they have been accepted as the standard codes for the 5G NR. In this paper, we propose two LDPC decoding algorithms: Hybrid Offset Min-Sum (HOMS) and Variable Offset Min-Sum (VOMS), which are aimed at improving the error correction performance. The main idea of the HOMS/VOMS algorithm is to apply modified factors to both variable-nodes and check-nodes updated processing in order to compensate the extrinsic messages overestimation of the MS-based algorithms and increase the protection ability for degree-1 variable-nodes. The simulation results show that at the Bit-Error-Rate (BER) of 10-5, the proposed HOMS/VOMS algorithm achieves the decoding gain up to 0.2 dB compared to the Offset Min-Sum (OMS) algorithm, with a slight increase in decoding complexity.

Today's modern wireless communication systems demand extensive quality and computational power with an increase in day-to-day data-rate standards. The latest com-munication standards focus on low latency, high throughput, and reliable error correction capabilities which inspired us to explore the 5G New Generation (NR) technology. Low-Density Parity-Check Codes (LDPC) are known to have error correction capabilities that can achieve Shannon's maximum channel ca-pacity. Encoding of LDPC Codes features a sparse property that enables effortless decoding at the receiver end. Advancements in deep learning have helped in estimating the channel noise more accurately. The Iterative Belief Propagation-Convolutional Neural Network (BP-CNN) architecture involves a CNN block which is trained with a quadratic loss function concatenated to a standard BP Decoder. The proposed Iterative BP-CNN architecture with a Batch Normalization layer results in a better performance compared to the Iterative BP-CNN architecture as it standardizes the input to the CNN block and also solves the problem of vanishing gradients during backpropagation.

Normalized Min-Sum Algorithms (NMSA) are extensively employed in trading LDPC (Low Density Parity Check) decoders due to their low complexity and reasonable performance close to the performance of sum product algorithm in terms of Error Rate. Our work is focused on the enhancement of error rate performances of NMS algorithm for the decoding of LDPC decoding. In this context we have proposed a Layered Normalized Min-Sum algorithm (LNMS), which employs an adaptive normalization factor to ameliorate the reliability of the information transmitted during the decoding process. To perform this analysis study LDPC coded communication system has been examined over Weibull fading channels and was analyzed for different decoding techniques by the help of comparative computer simulations. Simulation results indicate that the proposed decoding algorithm can achieve better Bit Error Rate (BER) performances closer to SP algorithm with the preservation of the principal characteristics of the MS algorithm.

Low-density parity-check (LDPC) codes have been selected as the channel coding scheme for 5G NR standard, which have excellent performance approaching the Shannon limit and are easy to implement in hardware. The decoding algorithm and scheduling scheme of LDPC codes have a significant impact on performance. The row degree (RD) and the number of punctured bits (PBs) are widely used to determine the update order of layers. In this letter, we used Matlab to simulate the error performance of the 5G LDPC codes. We completed the bit error rate and frame error rate simulations of six different decoding algorithms, including flooding LLR-BP, flooding NMS, layered LLR-BP, layered NMS, the lowest degree and least-punctured (LD-LP) layered LLR-BP and LD-LP layered NMS methods, for the 5G LDPC code with a base graph of size [46, 68], code rate 1/3, and code length of 1584.We further compared the performance of LD-LP layered decoding and LP-LD layered decoding. Moreover, we simulated the error performance of the core part of the LDPC code, which consists of four layers. We evaluated the effect of the update order of the four layers on the error performance of the code, and concluded that some update orders might give slightly better error performance than others.

Abstract In order to cater to the needs of the 5G standard, one of the prominent solutions in terms of high coding gain, high throughput and low power dissipation is the 5G NR LDPC (New Radio Low Density Parity Check) codes which have been adopted by 5G Standard. LDPC codes are the successful Third Generation Forward Error Correcting codes. An Efficient decoder is the key to the success of any Error Correcting Code. LDPC codes are one whose parity check matrix have a very few non zero entries. 5G NR LDPC codes are constructed by Protographs or base graphs and are block structured. This paper improves the performance of Layered Iterative minsum Approximation Message Passing decoding Algorithm using Rate Matching, Fixed Point Quantization and Offset minsum techniques. Rate Matching is to maintain the exact number of encoded blocks with in the TTI. Simulation of this algorithm with BPSK encoding over AWGN channel shows that BER of 10-3 gives Eb/No of~2 dB for the block length of 105.

Low-Density Parity-Check (LDPC) codes have been widely used in modern communication standards due to their strong error correction capabilities. This paper presents an experimental evaluation of a (1200, 600) irregular LDPC code over an additive white Gaussian noise (AWGN) channel, systematically comparing three decoding algorithms (Sum-Product, Normalized Min-Sum, and Offset Min-Sum) with three scheduling methods (Flooding, Layered Belief Propagation, and Residual Belief Propagation). Parameter sweeps are performed to determine the optimal normalization factor (

\alpha

) for the Normalized Min-Sum and the offset factor (

\beta

) for the Offset Min-Sum. A comparative analysis is then performed on the frame error rate (FER) and convergence behavior of each algorithm and scheduling configuration, considering the maximum number of iterations set at 10 and 25. The results show that the Offset Min-Sum algorithm with

\beta=0.5

and Layered Belief Propagation scheduling provides an acceptable trade-off between complexity and error-correction performance, closely matching the Sum-Product algorithm but at a lower computational cost. Although Residual Belief Propagation converges quickly at lower signal-to-noise ratios, it exhibits a high error floor. These findings provide practical guidelines for selecting optimal decoding configurations in resource-constrained applications.