A note on relationship between algebraic geometric codes and LDPC codes

Low-density parity-check (LDPC) codes constructed by a sparse parity-check matrix are of very fast encoding and decoding algorithms. Another kind of codes, which improved the well-known Gilbert-Varshamov bound, are algebraic geometry codes (Goppa geometry codes) from algebraic curves over finite fie...

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Bibliographische Detailangaben
Hauptverfasser:	Wanbao Hu, Huaping Cai, Yanxia Wu, Zhen Wang
Format:	Tagungsbericht
Sprache:	eng
Schlagworte:	algebraic geometry code (Goppa geometry code) Construction industry Error-correcting code Galois fields Geometry low-density parity-check (LDPC)code Null space Parity check codes Signal processing algorithms Sparse matrices
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Beschreibung
Zusammenfassung:	Low-density parity-check (LDPC) codes constructed by a sparse parity-check matrix are of very fast encoding and decoding algorithms. Another kind of codes, which improved the well-known Gilbert-Varshamov bound, are algebraic geometry codes (Goppa geometry codes) from algebraic curves over finite fields. In the note, we analyze their characteristic of the two class of codes and show that the algebraic geometric codes are seldom LDPC codes.
DOI:	10.1109/ICSPS.2010.5555509