In comparison to 4G, 5G wireless needs to support a broader range of applications. Therefore, both low-density parity-check (LDPC) codes and polar codes have been standardized by 5G new radio (NR) to fulfill the requirements of data channel and control channel, respectively. Usually, LDPC/polar decodings are implemented by separate hardware, leading to low area efficiency. Though decoders which can handle both codes have been proposed, how to compromise between throughput and efficiency has always been a persistent dilemma due to the absence of a unified and smooth integration methodology. To this end, by fully utilizing the common parts of graph-theoretic algorithms for both codes, this paper presents a unified decoder (UniDec) which is fully compatible with 5G NR LDPC/polar codes. This UniDec enables three key approaches:1) unified processing nodes for both codes,2) configurable permutation networks with multi-parallelism, and3) flexible scheduling for 5G NR parameter configuration, guaranteeing both high data throughput and area efficiency. Implemented in 40nm CMOS, the UniDec attains a maximum of$33.64\times $throughput and$5.98\times $area efficiency compared to its multi-mode counterparts. Even compared with the state-of-the-art (SOA) dedicated ones, the UniDec still maintains a competitive edge in terms of throughput, energy, and area efficiency. It is noted that this methodology can be generalized to other factor-graph based signal processing algorithms.

In this brief, a stochastic belief propagation (BP)-based iterative detection and decoding (IDD) for multiple-input and multiple-output (MIMO) system is proposed. We modify the algorithm of BP detection to make it more suitable for stochastic computation and enable the soft message to be transmitted between the detector and decoder in the format of stochastic sequences. Through IDD, the required number of iterations and quantization precision for the detector will decrease. By sharing the stochastic number generator, the hardware complexity of both the detector and decoder can be reduced. Hardware architectural optimizations and the corresponding implementation are also given, and we can implement 64 × 32, four-QAM MIMO system with (128, 64) polar codes with 1.283mm2area consumption. Compared with other detector, the hardware efficiency can be improved by 7.8 times.

Expectation propagation (EP) achieves excellent performance with high-order modulation in massive multiple-input multiple-output (MIMO) detection. The soft output of the EP detector can be iteratively combined with turbo soft decoders to enhance error-correction performance. However, the implementation of EP-based iterative detection and decoding (IDD) receivers suffer from an exponential increase in computational complexity as the number of antennas and modulation order grows. In this brief, we propose a simplified EP approximation-based IDD (sEPA-IDD) scheme for hardware implementation. To alleviate the computational burden, a simplified message update scheme is proposed, reducing complexity by 68% without performance degradation. Additionally, a unified design for extrinsic message computation further improves hardware utilization. Finally, we introduce the first unfolded EP-based IDD architecture to boost throughput. Compared with state-of-the-art (SOA) IDD receivers, the sEPA-IDD receiver implemented on 65 nm CMOS delivers a throughput of 3.07 Gb/s with a maximum 0.5 dB gain, achieving 4.03× higher throughput and 6.04× greater area efficiency.

Belief propagation (BP) decoding has natural advantages in throughput for polar codes to meet high-speed and low-latency requirements. The soft outputs of BP decoding can be utilized further for joint detection and decoding in the baseband communication system. However, its error-correction performance is not comparable with the successive cancellation list (SCL) decoding. Belief propagation flip (BPF) decoding is recently proposed to improve the error-correction performance of BP decoding and indicates the potential to compete with SCL decoding. In this paper, we propose an advanced BPF (A-BPF) scheme that reduces the decoding latency with the help of one critical bit and improves the error-correction performance by the proposed joint detection criterion. To improve area efficiency in the hardware level, an optimized sorting network is proposed and applied for the A-BPF decoder. The decoder is implemented on 65 nm CMOS technology for length-1024 and rate-1/2 polar codes, and the results show that the proposed decoder can achieve a close frame error rate performance to the SCL decoder with four lists and deliver a throughput of 5.17 Gb/s at Eb/N0= 4.0 dB.

For the scenarios with high throughput requirements, the belief propagation (BP) decoding is one of the most promising decoding strategies for polar codes. By pruning the redundant variable nodes (VNs) and check nodes (CNs) in the original factor graph, the graph is condensed to a sparse bipartite graph which is similar to the graph for low-density parity-check (LDPC) codes. In this paper, we introduce the bit-flipping scheme into the LDPC-like BP (L-BP) decoding and propose two methods to identify the error-prone VNs. By additional decoding attempts, the L-BP flip (L-BPF) decoding improves the error-rate performance with a similar average complexity for high Eb=N0values. The simulation results show that the L-BPF decoding achieves 0:25 dB gain compared with the L-BP decoding.

Since the inherent serial nature of successive cancellation list (SCL) decoding results in a long latency, belief propagation (BP) decoding for polar codes has drawn attention for high-throughput applications. However, its error correction performance is inferior to that of SCL decoding. Therefore, the bit-flipping strategy has been recently applied to BP decoding, which can approach the SCL decoding performance through multiple additional decoding attempts. The original BP flip (BPF) decoding suffers from an inaccurate identification of erroneous bits by a fixed flip set (FS), which has been improved by the generalized BPF (GBPF) decoding. In this article, the GBPF decoding is extended to support multiple bits being flipped in one decoding attempt. In addition, for two types of decoding errors: detected errors and undetected errors, we propose two novel methods to more effectively identify erroneous bits. For detected errors, the concept of loop sets is defined and a loopbased identification method is introduced based on the study of error patterns of BP decoding. On the other hand, a method to generate a more accurate fixed FS is proposed for undetected errors, which considers the bit error distribution under BP decoding. Combining the two methods, the GBPF with merged sets (GBPF-MS) decoding can achieve the SCL-8 performance and outperforms the state-of-the-art BPF, BP list, and SC flip (SCF) decoding, for polar codes with length 1024 and information rate 1/2. Implemented by 40nm CMOS technology, the proposed GBPF-MS decoder with ten flips exhibits an average throughput of 4.19 Gbps at 2.5 dB, which is 1.6× and 1.72× faster than the state-of-the-art SCL-4 and SCF decoders, respectively.