We present an encoding scheme of a single logical qubit with single-sided quantum dot (QD)-cavity systems, which is immune to the collective decoherence. By adjusting the Purcell factor to satisfy the balanced reflection condition, the detrimental effects of unbalanced reflection between the coupled and uncoupled QD-cavity systems can be effectively suppressed. Furthermore, the fidelity of each step can be increased to unity regardless of the strong coupling regime and the weak coupling regime of cavity quantum electrodynamics (QED) with the assistance of waveform correctors. The scheme requires QD-cavity systems and simple linear optical elements, which can be implemented with the currently experimental techniques.