Performance Limits and Practical Decoding of Interleaved Reed-Solomon Polar Concatenated Codes
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar cod...
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| Veröffentlicht in: | IEEE transactions on communications Jg. 62; H. 5; S. 1406 - 1417 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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New York, NY
IEEE
01.05.2014
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0090-6778, 1558-0857 |
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| Abstract | A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any ε > 0, and total frame length N, the parameters of the scheme can be set such that the frame error probability is less than 2 -N1-ε , while the scheme is still capacity achieving. This improves upon 2 -N0.5-ε , the frame error probability of Arikan's polar codes. The proposed concatenated polar codes and Arikan's polar codes are also compared for transmission over channels with erasure bursts. We provide a sufficient condition on the length of erasure burst which guarantees failure of the polar decoder. On the other hand, it is shown that the parameters of the concatenated polar code can be set in such a way that the capacity-achieving properties of polar codes are preserved. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity. |
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| AbstractList | A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any ε > 0, and total frame length N, the parameters of the scheme can be set such that the frame error probability is less than 2 -N1-ε , while the scheme is still capacity achieving. This improves upon 2 -N0.5-ε , the frame error probability of Arikan's polar codes. The proposed concatenated polar codes and Arikan's polar codes are also compared for transmission over channels with erasure bursts. We provide a sufficient condition on the length of erasure burst which guarantees failure of the polar decoder. On the other hand, it is shown that the parameters of the concatenated polar code can be set in such a way that the capacity-achieving properties of polar codes are preserved. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity. A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any [straight epsilon] > 0, and total frame length N, the parameters of the scheme can be set such that the frame error probability is less than 2^{-N^{1-[straight epsilon]}}, while the scheme is still capacity achieving. This improves upon 2^{-N^{0.5-[straight epsilon]}}, the frame error probability of Arikan's polar codes. The proposed concatenated polar codes and Arikan's polar codes are also compared for transmission over channels with erasure bursts. We provide a sufficient condition on the length of erasure burst which guarantees failure of the polar decoder. On the other hand, it is shown that the parameters of the concatenated polar code can be set in such a way that the capacity-achieving properties of polar codes are preserved. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity. A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any epsilon > 0, and total frame length N, the parameters of the scheme can be set such that the frame error probability is less than 2-N1- epsilon }}, while the scheme is still capacity achieving. This improves upon 2-N0.5- epsilon }}, the frame error probability of Arikan's polar codes. The proposed concatenated polar codes and Arikan's polar codes are also compared for transmission over channels with erasure bursts. We provide a sufficient condition on the length of erasure burst which guarantees failure of the polar decoder. On the other hand, it is shown that the parameters of the concatenated polar code can be set in such a way that the capacity-achieving properties of polar codes are preserved. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity. |
| Author | Mahdavifar, Hessam Jungwon Lee Inyup Kang El-Khamy, Mostafa |
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| Keywords | Reed Solomon code Performance evaluation Error probability generalized minimum distance Error estimation capacity-achieving codes Error rate Transmission channel Concatenated codes Decoding Algorithm Binary code Failures Polar codes burst erasures Reed-Solomon codes Gilbert-Elliot Concatenation Sufficient condition error exponent Algorithm complexity Interleaved codes Minimal distance Polar code |
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| SubjectTerms | Applied sciences Block codes burst erasures Bursts capacity-achieving codes Channels Codes Coding, codes Complexity theory Concatenated codes Decoding Error analysis error exponent Error probability Errors Exact sciences and technology Frames generalized minimum distance Gilbert-Elliot Information, signal and communications theory Mathematical analysis Polar codes Reed-Solomon codes Signal and communications theory Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) |
| Title | Performance Limits and Practical Decoding of Interleaved Reed-Solomon Polar Concatenated Codes |
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