  We propose a belief propagation list (BPL) decoder with comparable
performance to the successive cancellation list (SCL) decoder of polar codes,
which already achieves the maximum likelihood (ML) bound of polar codes for
sufficiently large list size $L$. The proposed decoder is composed of multiple
parallel independent belief propagation (BP) decoders based on differently
permuted polar code factor graphs. A list of possible transmitted codewords is
generated and the one closest to the received vector, in terms of Euclidean
distance, is picked. To the best of our knowledge, the proposed BPL decoder
provides the best performance of plain polar codes under iterative decoding
known so far. The proposed algorithm does not require any changes in the polar
code structure itself, rendering the BPL into an alternative to the SCL
decoder, equipped with a soft output capability enabling, e.g., iterative
detection and decoding to further improve performance. Further benefits are
lower decoding latency compared to the SCL decoder and the possibility of high
throughput implementations. Additionally, we show that a different selection
strategy of frozen bit positions can further enhance the error-rate performance
of the proposed decoder.
