Variant belief-propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes, and a near Shannon limit error-rate performance is obtained. However, the decoders presented in previous literature suffer from a large resource consumption due to the accumulative calculations for each extrinsic message updating. In this paper, check belief is introduced as the probability that the corresponding parity check is satisfied. A check belief propagation (CBP) algorithm is proposed, which can force all the check nodes to contribute their check beliefs to others in a sequential order. The check nodes will enlarge the check beliefs of all the check nodes iteratively. This can result in positive check beliefs for all the check nodes, which indicates that all the parity checks are successfully satisfied. Different from previous BP algorithms, the check beliefs are propagated with no accumulative calculations at an acceptable speed, with low complexity and without performance loss. The simulation results and analyses show that the CBP algorithm provides a similar prominent error-rate performance as the previous BP algorithms, but consumes a lot fewer resources than them. It earns a big benefit in terms of complexity.

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