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.

翻译：变体置信传播（BP）算法被应用于低密度奇偶校验（LDPC）码，可获得接近香农极限的误码率性能。然而，以往文献中提出的译码器由于每次外部消息更新时的累加计算，导致资源消耗较大。本文引入校验置信度作为相应奇偶校验得到满足的概率，提出了一种校验置信传播（CBP）算法。该算法能够强制所有校验节点按序将其校验置信度传递给其他节点，并通过迭代方式逐步增大所有校验节点的校验置信度，最终使所有校验节点获得正值校验置信度，表明所有奇偶校验均成功满足。与以往BP算法不同，CBP算法在无累加计算的情况下以可接受的速度传播校验置信度，具有低复杂度且无性能损失。仿真结果与分析表明，CBP算法虽能提供与以往BP算法相当优异的误码率性能，但资源消耗显著降低，在复杂度方面具有显著优势。