Mutual Constrained Min-Sum Check-Belief Propagation for 5G LDPC Codes: Algorithm and Implementation

State-of-the-art (SOA) designs for 5G New Radio (NR) low-density parity-check (LDPC) face a dilemma: enduring the high complexity of cumulative calculations or accepting performance degradation from unreliable messages for degree-1 variable nodes (VNs). This paper introduces the mutual constrained min-sum check-belief propagation (MCMS-CBP) decoding algorithm to resolve this dilemma. By establishing the mutual constrained cycle in well-designed message updating, while incorporating the constraint compensation strategy, the non-cumulative MCMS-CBP substantially improves the reliability of check-belief to variable-node messages for degree-1 VNs. Numerical results show that fixed-point MCMS-CBP maintains a gap of less than 0.1 dB compared to floating-point flooding belief propagation decoding algorithm across various 5G NR LDPC codes and offers inherently low complexity for hardware implementation. In addition, this paper presents an area-throughput efficient 5G NR LDPC decoder which is based on fixed-point MCMS-CBP and supports all 5G NR LDPC codes. Key techniques for optimizing the area and latency of decoder include: the sign-bit storage, reducing memory overhead by 87.5%; the intra-layer first block schedule, eliminating pipeline stalls;the partially aligned element arrangement, halving the cyclic shifter cost while eliminating memory pre-writeback rotation. Implementation result on SMIC 28nm technology demonstrates that the proposed decoder has a cell area of 1.610 mm$\boldsymbol {^{2}}$and a peak throughput of 58.63 Gbps, yielding a 36.42 Gbps/mm$\boldsymbol {^{2}}$maximum area efficiency that is$\boldsymbol {2.72\times }$higher than SOA LDPC decoders.