Employing heavy conventional encryption algorithms in communications suffers from added overhead and processing time delay; and in wireless communications, in particular, suffers from severe performance deterioration (avalanche effect) due to fading. Consequently, a tremendous reduction in data throughput and increase in complexity and time delay may occur especially when information traverse resource-limited devices as in Internet-of-Things (IoT) applications. To overcome these drawbacks, efficient lightweight encryption algorithms have been recently proposed in literature. One of those, that is of particular interest, requires using conventional encryption only for the first block of data in a given frame being transmitted. All the information in the remaining blocks is transmitted securely without the need for using heavy conventional encryption. Unlike the conventional encryption algorithms, this particular algorithm achieves lower overhead/complexity and higher data throughput. Assuming the additive white Gaussian noise (AWGN) channel, the performance of the lightweight encryption algorithm under study had been evaluated in literature in terms of throughput under the assumption that the first block, that undergoes conventional encryption, is free of error, which is practically unfeasible. In this paper, we consider the AWGN channel with Rayleigh fading and assume that the signal experiences a certain channel bit error probability and investigate the performance of the lightweight encryption algorithm under study in terms of bit error probability and throughput. We derive analytical expressions for these performance metrics considering modulated signals with and without coding. In addition, we propose an extension to the lightweight encryption algorithm under study by further enhancing its security level without significantly affecting the overhead size and processing time. Via numerical results we show the superiority of the lightweight encryption algorithm under study over the conventional encryption algorithms (like the AES) and the lightweight encryption algorithms proposed in literature in terms of error and throughput performance.