  Variant belief propagation (BP) algorithms are applied to low-density
parity-check (LDPC) codes. However, conventional decoders suffer from a large
resource consumption due to gathering messages from all the neighbour
variable-nodes and/or check-nodes through cumulative calculations. In this
paper, a check-belief propagation (CBP) decoding algorithm is proposed.
Check-belief is used as the probability that the corresponding parity-check is
satisfied. All check-beliefs are iteratively enlarged in a sequential recursive
order, and successful decoding will be achieved after the check-beliefs are all
big enough. Compared to previous algorithms employing a large number of
cumulative calculations to gather all the neighbor messages, CBP decoding can
renew each check-belief by propagating it from one check-node to another
through only one variable-node, resulting in a low complexity decoding with no
cumulative calculations. The simulation results and analyses show that the CBP
algorithm provides little error-rate performance loss in contrast with the
previous BP algorithms, but consumes much fewer calculations and memories than
them. It earns a big benefit in terms of complexity.
