Finite Alphabet Iterative Decoders-Part I: Decoding Beyond Belief Propagation on the Binary Symmetric Channel
We introduce a new paradigm for finite precision iterative decoding on low-density parity-check codes over the binary symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are quantized versions of the belief propagation (BP) decoder, the...
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| Vydáno v: | IEEE transactions on communications Ročník 61; číslo 10; s. 4033 - 4045 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York, NY
IEEE
01.10.2013
Institute of Electrical and Electronics Engineers |
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| ISSN: | 0090-6778 |
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| Abstract | We introduce a new paradigm for finite precision iterative decoding on low-density parity-check codes over the binary symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are quantized versions of the belief propagation (BP) decoder, the proposed finite alphabet iterative decoders (FAIDs) do not propagate quantized probabilities or log-likelihoods and the variable node update functions do not mimic the BP decoder. Rather, the update functions are maps designed using the knowledge of potentially harmful subgraphs that could be present in a given code, thereby rendering these decoders capable of outperforming the BP in the error floor region. On certain column-weight-three codes of practical interest, we show that there exist {FAIDs that surpass the floating-point BP decoder in the error floor region while requiring only three bits of precision for the representation of the messages}. Hence, FAIDs are able to achieve a superior performance at much lower complexity. We also provide a methodology for the selection of FAIDs that is not code-specific, but gives a set of candidate FAIDs containing potentially good decoders in the error floor region for any column-weight-three code. We validate the code generality of our methodology by providing particularly good three-bit precision FAIDs for a variety of codes with different rates and lengths. |
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| AbstractList | We introduce a new paradigm for finite precision iterative decoding on low-density parity-check codes over the binary symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are quantized versions of the belief propagation (BP) decoder, the proposed finite alphabet iterative decoders (FAIDs) do not propagate quantized probabilities or log-likelihoods and the variable node update functions do not mimic the BP decoder. Rather, the update functions are maps designed using the knowledge of potentially harmful subgraphs that could be present in a given code, thereby rendering these decoders capable of outperforming the BP in the error floor region. On certain column-weight-three codes of practical interest, we show that there exist {FAIDs that surpass the floating-point BP decoder in the error floor region while requiring only three bits of precision for the representation of the messages}. Hence, FAIDs are able to achieve a superior performance at much lower complexity. We also provide a methodology for the selection of FAIDs that is not code-specific, but gives a set of candidate FAIDs containing potentially good decoders in the error floor region for any column-weight-three code. We validate the code generality of our methodology by providing particularly good three-bit precision FAIDs for a variety of codes with different rates and lengths. |
| Author | Declercq, David Planjery, Shiva Kumar Danjean, Ludovic Vasic, Bane |
| Author_xml | – sequence: 1 givenname: Shiva Kumar surname: Planjery fullname: Planjery, Shiva Kumar email: shivap@email.arizona.edu organization: ETIS Lab., Univ. de Cergy-Pontoise, Cergy-Pontoise, France – sequence: 2 givenname: David surname: Declercq fullname: Declercq, David email: declercq@ensea.fr organization: ETIS Lab., Univ. de Cergy-Pontoise, Cergy-Pontoise, France – sequence: 3 givenname: Ludovic surname: Danjean fullname: Danjean, Ludovic email: danjean@ece.arizona.edu organization: Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ, USA – sequence: 4 givenname: Bane surname: Vasic fullname: Vasic, Bane email: vasic@ece.arizona.edu organization: Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ, USA |
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| Keywords | Alphabet Performance evaluation Binary channel belief propagation Logarithmic function binary symmetric channel error floor Updating trapping sets Iterative decoding Credal approach Trapping Low-density parity-check codes Subgraph Floating point Error correcting code Parity check codes finite precision iterative decoding |
| Language | English |
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| References | ref13 ref34 ref37 ref15 ref36 ref14 richardson (ref3) 0 ref31 diao (ref7) 0 ref33 ref11 ref32 ref10 (ref39) 0 ref17 ref16 ref19 ref18 tanner (ref30) 0 declercq (ref35) 0 kurkoski (ref12) 0 ref24 ref23 ref26 ref25 ref20 ref22 ref21 gallager (ref1) 1963 (ref38) 0 ref28 ref27 ref29 ref8 ref9 ref4 ref6 ref5 pearl (ref2) 1988 |
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| SubjectTerms | Applied sciences Arrays Belief propagation binary symmetric channel Charge carrier processes Coding, codes Computer Science Decoding error floor Exact sciences and technology finite precision iterative decoding Information Theory Information, signal and communications theory Iterative decoding Low-density parity-check codes Quantization (signal) Signal and communications theory Telecommunications and information theory trapping sets |
| Title | Finite Alphabet Iterative Decoders-Part I: Decoding Beyond Belief Propagation on the Binary Symmetric Channel |
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