Generator Matrix Design for Enhanced Distance Linear Block Code in Deep Space Missions

Abstract

Introduction: In this article, modified linear block codes (MLBCs) are constructed from a completely controllable discrete-time system. These codes are systematic codes where the information part and the parity part of the codes are explicitly separate. In this research, a new variant of block code using permutation arrays is designed. The MLBCs are designed to possess the best possible minimum distance characteristic which in turn leads to error correcting codes with good error correction capability. The constructed generator matrix for the designed MLBCs is developed with the help of distance-increasing mapping (DIM). DIM is established using permutation arrays (PAs) of binary vectors which are obtained from the solution space of a control system. The performance of the developed MLBCs is verified. The probability of undetected errors which is one of the key features of Error Correcting Codes is found to be higher than the Linear Block Codes. The designed code is decodable using the existing decoding algorithms. Constructed codes in this article can be used in high frequency radio environment for deep space mission.