DS-LDPC Codes

Verification of the effectiveness
of DS-LDPC codes
for memory applications
M. Pilar Vélez
22 de junio de 2016
Encuentro de Algebra Computacional y Aplicaciones - EACA 2016
Logroño, 22-24 de junio de 2016
DS-LDPC Codes
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Defining a DS-LDPC code
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Error-correcting
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Detecting errors: Check-sums
Codeword
Error vector
Received word
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Detecting errors
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Example
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Conjecture
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Theorem
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Notation and Remark
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Proof of the theorem (odd number of errors)
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Proof of the theorem (two errors)
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Proof of the theorem (two errors)
Contradiction
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Proof of the theorem (four errors)
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Proof of the theorem (four errors)
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Proof of the theorem (four errors)
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Proof of the theorem (four errors)
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Appendix: Perfect difference linear equations
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez
Conclusions
Verification of the effectiveness of DS-LDPC codes for memory applications
R. Rubio, J.M. Serradilla & M. P. Vélez