Belief Propagation (BP) algorithm is suitable for high-throughput decoding of polar codes due to its inherent parallelism. However, compared with Successive Cancellation (SC)-based decoding methods, BP-based schemes fall behind in terms of Bit-Error Rate (BER) performance. In this paper, a simplified stage-combined BP decoding algorithm is proposed that not only reduces decoding latency, but also improves BER performance. Theoretically, decoding latency can be halved with the proposed method, while the BER performance could be improved by 1 dB in some instances of polar codes. Furthermore, the average number of iterations for achieving a specific BER performance is either reduced or remains the same as the baseline decoding method.

The key computation in the min-sum decoding algorithm of a Low-Density Parity-Check (LDPC) code is finding the first two minima and also the location of the first minimum among a set of messages passed from Variable Nodes (VNs) to Check Nodes (CNs) in a Tanner graph. In this paper, we propose a modified rejection-based scheme for this task which is able to find the one-hot sequence of the minimum location instead of its index. We show that this modification effectively reduces the complexity of min-sum decoding algorithm. Additionally, we reveal a pipelining potential in such a rejection- based architecture which facilitates the multi-frame decoding of LDPC codes and therefore results in improvement in decoding throughput with bearable hardware overhead. Synthesis in an industrial 28nm CMOS technology shows improved results in terms of throughput, power, and chip area.