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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Veröffentlicht in:IEEE transactions on communications Jg. 61; H. 10; S. 4033 - 4045
Hauptverfasser: Planjery, Shiva Kumar, Declercq, David, Danjean, Ludovic, Vasic, Bane
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.10.2013
Institute of Electrical and Electronics Engineers
Schlagworte:
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
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
ISSN:0090-6778
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Beschreibung
Zusammenfassung: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.
ISSN:0090-6778
DOI:10.1109/TCOMM.2013.090513.120443