  Belief propagation (BP) is an iterative decoding algorithm for polar codes
which can be parallelized effectively to achieve higher throughput. However,
because of the presence of error floor due to cycles and stopping sets in the
factor graph, the performance of the BP decoder is far from the performance of
state of the art cyclic redundancy check (CRC) aided successive cancellation
list (CA-SCL) decoders. It has been shown that successive BP decoding on
multiple permuted factor graphs, which is called the multi-trellis BP decoder,
can improve the error performance. However, when permuting the entire factor
graph, since the decoder dismisses the information from the previous
permutation, the number of iterations required is significantly larger than
that of the standard BP decoder. In this work, we propose a new variant of the
multi-trellis BP decoder which permutes only a subgraph of the original factor
graph. This enables the decoder to retain information of variable nodes in the
subgraphs, which are not permuted, reducing the required number of iterations
needed in-between the permutations. As a result, the proposed decoder can
perform permutations more frequently, hence being more effective in mitigating
the effect of cycles which cause oscillation errors. Experimental results show
that for a polar code with block length 1024 and rate 0.5 the error performance
gain of the proposed decoder at the frame error rate of 10^(-6) is 0.25 dB
compared to multi-trellis decoder based on full permutations. This performance
gain is achieved along with reduced latency in terms of the number of
iterations.
