Polar codes are newly discovered capacity-achieving codes, which haveattracted lots of research efforts. Polar codes can be efficiently decoded bythe low-complexity successive cancelation (SC) algorithm and the SC list (SCL)decoding algorithm. The belief propagation (BP) decoding algorithm not only isan alternative to the SC and SCL decoders, but also provides soft outputs thatare necessary for joint detection and decoding. Both the BP decoder and thesoft cancelation (SCAN) decoder were proposed for polar codes to output softinformation about the coded bits. In this paper, first a belief propagationdecoding algorithm, called reduced complexity soft cancelation (RCSC) decodingalgorithm, is proposed. Let $N$ denote the block length. Our RCSC decodingalgorithm needs to store only $5N-3$ log-likelihood ratios (LLRs),significantly less than $4N-2+\frac{N\log_2N}{2}$ and $N(\log_2N+1)$ LLRsneeded by the BP and SCAN decoders, respectively, when $N\geqslant 64$.Besides, compared to the SCAN decoding algorithm, our RCSC decoding algorithmeliminates unnecessary additions over the real field. Then the simplified SC(SSC) principle is applied to our RCSC decoding algorithm, and the resultingSSC-aided RCSC (S-RCSC) decoding algorithm further reduces the computationalcomplexity. Finally, based on the S-RCSC decoding algorithm, we propose acorresponding memory efficient decoder architecture, which has better errorperformance than existing architectures. Besides, our decoder architectureconsumes less energy on updating LLRs.
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