95 research outputs found
Belief Propagation Decoding of Polar Codes on Permuted Factor Graphs
We show that the performance of iterative belief propagation (BP) decoding of
polar codes can be enhanced by decoding over different carefully chosen factor
graph realizations. With a genie-aided stopping condition, it can achieve the
successive cancellation list (SCL) decoding performance which has already been
shown to achieve the maximum likelihood (ML) bound provided that the list size
is sufficiently large. The proposed decoder is based on different realizations
of the polar code factor graph with randomly permuted stages during decoding.
Additionally, a different way of visualizing the polar code factor graph is
presented, facilitating the analysis of the underlying factor graph and the
comparison of different graph permutations. In our proposed decoder, a high
rate Cyclic Redundancy Check (CRC) code is concatenated with a polar code and
used as an iteration stopping criterion (i.e., genie) to even outperform the
SCL decoder of the plain polar code (without the CRC-aid). Although our
permuted factor graph-based decoder does not outperform the SCL-CRC decoder, it
achieves, to the best of our knowledge, the best performance of all iterative
polar decoders presented thus far.Comment: in IEEE Wireless Commun. and Networking Conf. (WCNC), April 201
CRC-Aided Belief Propagation List Decoding of Polar Codes
Although iterative decoding of polar codes has recently made huge progress
based on the idea of permuted factor graphs, it still suffers from a
non-negligible performance degradation when compared to state-of-the-art
CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show
that iterative decoding of polar codes based on the belief propagation list
(BPL) algorithm can approach the error-rate performance of CA-SCL decoding and,
thus, can be efficiently used for decoding the standardized 5G polar codes.
Rather than only utilizing the cyclic redundancy check (CRC) as a stopping
condition (i.e., for error-detection), we also aim to benefit from the
error-correction capabilities of the outer CRC code. For this, we develop two
distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv
(BCJR)-based approach and a sum product algorithm (SPA)-based approach.
Further, an optimized selection of permuted factor graphs is analyzed and shown
to reduce the decoding complexity significantly. Finally, we benchmark the
proposed CRC-aided belief propagation list (CA-BPL) to state-of-the-art 5G
polar codes under CA-SCL decoding and, thereby, showcase an error-rate
performance not just close to the CA-SCL but also close to the maximum
likelihood (ML) bound as estimated by ordered statistic decoding (OSD).Comment: Submitted to IEEE for possible publicatio
On the Decoding of Polar Codes on Permuted Factor Graphs
Polar codes are a channel coding scheme for the next generation of wireless
communications standard (5G). The belief propagation (BP) decoder allows for
parallel decoding of polar codes, making it suitable for high throughput
applications. However, the error-correction performance of polar codes under BP
decoding is far from the requirements of 5G. It has been shown that the
error-correction performance of BP can be improved if the decoding is performed
on multiple permuted factor graphs of polar codes. However, a different BP
decoding scheduling is required for each factor graph permutation which results
in the design of a different decoder for each permutation. Moreover, the
selection of the different factor graph permutations is at random, which
prevents the decoder to achieve a desirable error-correction performance with a
small number of permutations. In this paper, we first show that the
permutations on the factor graph can be mapped into suitable permutations on
the codeword positions. As a result, we can make use of a single decoder for
all the permutations. In addition, we introduce a method to construct a set of
predetermined permutations which can provide the correct codeword if the
decoding fails on the original permutation. We show that for the 5G polar code
of length , the error-correction performance of the proposed decoder is
more than dB better than that of the BP decoder with the same number of
random permutations at the frame error rate of
Decoding Reed-Muller Codes Using Redundant Code Constraints
The recursive projection-aggregation (RPA) decoding algorithm for Reed-Muller (RM) codes was recently introduced by Ye and Abbe. We show that the RPA algorithm is closely related to (weighted) belief-propagation (BP) decoding by interpreting it as a message-passing algorithm on a factor graph with redundant code constraints. We use this observation to introduce a novel decoder tailored to high-rate RM codes. The new algorithm relies on puncturing rather than projections and is called recursive puncturing-aggregation (RXA). We also investigate collapsed (i.e., non-recursive) versions of RPA and RXA and show some examples where they achieve similar performance with lower decoding complexity
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