  This study focuses on the efficiency of message-passing-based decoding
algorithms for polar and low-density parity-check (LDPC) codes. Both successive
cancellation (SC) and belief propagation (BP) decoding algorithms are studied
{in} the message-passing framework. Counter-intuitively, SC decoding
demonstrates the highest decoding efficiency, although it was considered a weak
decoder {in terms of} error-correction performance. We analyze the
complexity-performance tradeoff to dynamically track the decoding efficiency,
where the complexity is measured by the number of messages passed (NMP), and
the performance is measured by the statistical distance to the maximum a
posteriori (MAP) estimate. This study offers a new insight into the
contribution of each message passed in decoding, and compares various decoding
algorithms on a message-by-message level. The analysis corroborates recent
results on terabits-per-second polar SC decoders, and might shed light on
better scheduling strategies.
