Generalized Systematic Comma-Free Code

Abstract

In channels that introduce substitution, insertion, and deletion errors, one challenging problem for a code designer to overcome is to avoid false code-synchronization. In other words, the probability of a false codeword occurring should be minimized with appropriate code designs. In this paper, we propose a new class of systematic comma-free code called generalized $F(n,s,t)$ code for channels that are impaired by substitution, insertion, and deletion errors. We first prove that this code is a synchronous code and then we derive the probabilities of false synchronization when a substitution, insertion, or deletion error occurs. We compare the theoretical and simulation results under different channel parameters. We also analyze the factors affecting the false synchronization for each case. The proposed code gives a higher code efficiency and better choice in terms of false synchronization compared with the classical F codes.