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

TL;DR

This paper introduces an algorithm leveraging Karnaugh maps to efficiently detect and correct multiple errors in data transmission, improving error correction capabilities and reducing computational complexity.

Contribution

It presents a novel algorithm that reduces occupied squares in Karnaugh maps, enabling faster error detection and correction, including for burst errors.

Findings

Algorithm effectively corrects two simultaneous errors.

Reduced execution time for data bit placement.

Systematic coding for burst error correction.

Abstract

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.