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

Outer Channel of DNA-Based Data Storage: Capacity and Efficient Coding Schemes

In this paper, we consider the outer channel for DNA-based data storage, where each DNA string is either correctly transmitted, or being erased, or being corrupted by uniformly distributed random substitution errors, and all strings are randomly shuffled with each other. We first derive the capacity of the outer channel, which surprisingly implies that the uniformly distributed random substitution errors are only as harmful as the erasure errors. Next, we propose efficient coding schemes which encode the bits at the same position of different strings into a codeword. We compute the soft/hard information of each bit, which allows us to independently decode the bits within a codeword, leading to an independent decoding scheme. To improve the decoding performance, we measure the reliability of each string based on the independent decoding result, and perform a further step of decoding over the most reliable strings, leading to a joint decoding scheme. Simulations with low-density parity-check codes confirm that the joint decoding scheme can reduce the frame error rate by more than 3 orders of magnitude compared to the independent decoding scheme, and it can outperform the state-of-the-art decoding scheme in the literature in a wide parameter regions.Comment: This paper has been submitted to IEEE Trans. Inf. Theor