Abstract
For finite-length polar codes, the standard successive cancellation (SC) decoding has been improved, such as SC-List (SCL), SC-Stack (SCS), and SC-Flip (SCF) decodings. In this paper, we present an alternative improvement of SC decoding by incorporating the Fano sequential decoding into SC decoding. This is referred to as SC-Fano decoding. Specifically, it can address the major drawback of SC decoding by enabling moving-backward when the reliability of an on-going path is not good enough. The SCS and SC-Fano decodings can be viewed as the sequential decoding for polar codes. In addition, for cyclic-redundancy-check (CRC) concatenated polar codes, we enhance SC-Fano decoding by leveraging the bit-flipping idea of SCF decoding. The simulation results demonstrate that the proposed SC-Fano decoding can provide better performance-complexity tradeoff than the existing decoding methods.
Highlights
Polar codes, proposed by Arikan in [1], achieve the symmetric capacity of the binary-input discrete memoryless channels (BI-DMCs) under a low-complexity successive-cancellation (SC) decoding
THE PROPOSED SC-FANO DECODING We propose a low-complexity SC-Fano decoding for polar codes, by incorporating the Fano sequential decoding [14] into the standard SC decoding
We develop the so-called SCF-Fano decoding for CRC-concatenated polar codes, by combining SC-Fano decoding with the bit-flipping idea of SCF decoding
Summary
Polar codes, proposed by Arikan in [1], achieve the symmetric capacity of the binary-input discrete memoryless channels (BI-DMCs) under a low-complexity successive-cancellation (SC) decoding. In spite of its computational advantage, SCS decoding requires larger space-complexity and its performance is poor when the stacksize is small [3], [4]. Another improvement of SC decoding was proposed in [7] with the aid of cyclic-redundancy-check. (CRC) code, which is referred to as SC-Flip (SCF) decoding In this method, SC decoding is first performed to generate an initial estimated codeword. The additional SC decoding proceeds by flipping a single information-bit corresponding to the lowest log-likelihood ratios (LLRs) This process is repeated until either a valid codeword is found (i.e., CRC passes) or a maximum number of iterations (i.e., Tmax ) is performed.
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