Designing of Increased Distance Modified Linear Block Code with its Decoding Algorithm using Syndrome Polynomial

Abstract

Introduction: This article gives the designing of increased distance modified linear block code (MLBC). Designing of this MLBC is initially obtained from the basis vectors an Upper Triangular Matrix (UTM).  Considered UTM is of 9^th order. Using the basis vectors of a 9^th order UTM, MLBC is established which has less minimum distance (d_min) between the codewords. A new approach is developed to increase this d_min with the help of distance increasing mapping (DIM). The developed code here for 9^th order UTM is (18, 9, d_min = 5) code. A decoding algorithm is designed to decode the errors in the transmission with the help of syndrome polynomials. The developed algorithm avoids the limitation of multiple solutions and Maximum Likelihood decoding associated with Linear Block Codes. Performance of this code has been established through simulation. Examples are explored here to decode the various bit positional errors if occurred during the transmission process with the help of developed decoding algorithm through simulation. These designed codes can be used in high-frequency radio environments for transmission and reception of signals.