Data Bits in Karnaugh Map and Increasing Map Capability in Error Correcting

To provide reliable communication in data transmission, ability of correcting errors is of prime importance. This paper intends to suggest an easy algorithm to detect and correct errors in transmission codes using the well-known Karnaugh map. Referring to past research done and proving new theorems and also using a suggested simple technique taking advantage of the easy concept of Karnaugh map, we offer an algorithm to reduce the number of occupied squares in the map and therefore, reduce substantially the execution time for placing data bits in Karnaugh map. Based on earlier papers, we first propose an algorithm for correction of two simultaneous errors in a code. Then, defining specifications for empty squares of the map, we limit the choices for selection of new squares. In addition, burst errors in sending codes is discussed, and systematically code words for correcting them will be made.

[1]  Osnat Keren One-to-Many: Context-Oriented Code for Concurrent Error Detection , 2010, J. Electron. Test..

[2]  Chin-Long Chen Error-Correcting Codes with Byte Error-Detection Capability , 1983, IEEE Transactions on Computers.

[3]  Dhiraj K. Pradhan,et al.  Single error correctable bit parallel multipliers over GF(2m) , 2009, IET Comput. Digit. Tech..

[4]  M. Rudelson,et al.  Geometric approach to error-correcting codes and reconstruction of signals , 2005, math/0502299.

[5]  Hamid Jafarkhani,et al.  Interference Mitigation Using Asynchronous Transmission and Sampling Diversity , 2016, 2016 IEEE Global Communications Conference (GLOBECOM).

[6]  Chin-Long Chen,et al.  Error-Correcting Codes with Byte Error-Detection Capability , 1983, IEEE Trans. Computers.

[7]  Paul H. Siegel,et al.  On codes that correct asymmetric errors with graded magnitude distribution , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[8]  Khaled A. S. Abdel-Ghaffar,et al.  Error-Correcting Codes for Flash Coding , 2011, IEEE Transactions on Information Theory.

[9]  L. Litwin,et al.  Error control coding , 2001 .

[10]  R. Morelos-Zaragoza The art of error correcting coding , 2002 .

[11]  Nikil D. Dutt,et al.  Dependability evaluation of SISO control-theoretic power managers for processor architectures , 2017, 2017 IEEE Nordic Circuits and Systems Conference (NORCAS): NORCHIP and International Symposium of System-on-Chip (SoC).

[12]  Torleiv Kløve,et al.  Codes for Error Detection , 2007, Series on Coding Theory and Cryptology.

[13]  Rabab Kreidieh Ward,et al.  Error Correction and Detection, a Geometric Approach , 1984, Comput. J..

[14]  Pedro Reviriego,et al.  Soft error detection and correction for FFT based convolution using different block lengths , 2009, 2009 15th IEEE International On-Line Testing Symposium.

[15]  Moshe Schwartz,et al.  Quasi-Cross Lattice Tilings With Applications to Flash Memory , 2011, IEEE Transactions on Information Theory.

[16]  Dimitris Nikolos,et al.  Theory and Design of t-Error Correcting/d-Error Detecting (d>t) and All Unidirectional Error Detecting Codes , 1991, IEEE Trans. Computers.