## 1 Introduction  
The development of high-speed, secure optical communication has been an important field of research in recent times and has been gaining momentum due to both the requirement scenario and the relevant technological advances [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. The possibility of realizing secure optical communication using chaotic laser systems has attracted much attention after the realization of chaos synchronization in nonlinear systems [12]. Semiconductor diode lasers are best suited devices to produce broadband chaotic output and, thus, enable optical encoding and decoding processes [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. A typical secure optical communication scheme involves two semiconductor lasers acting as transmitter laser (TL) and receiver laser (RL), in which the transmitter's output intensity is rendered chaotic through optical feedback. Messages masked in the chaotic output of the transmitter can be decoded at the receiver, by achieving synchronization between TL and RL optical outputs. In solid-state lasers, the encoding and decoding binary bit-sequences had been demonstrated by [PERSON] and [PERSON] [33]. A square wave message embedded with erbium-doped fiber ring laser, where the chaotic signal generated by optical feedback, was experimentally demonstrated in 1998 [1]. Message encoding and decoding using a system of chaotic external-cavity semiconductor lasers have been demonstrated [34].  
Chaos communications using semiconductor lasers with optical feedback, optical injection locking, and optoelectronic feedback were reported, and compared [19; 35].  
Chaos modulation (CMO) [1; 36; 37; 38], chaos masking (CMA) [39; 40; 41], and chaos shift keying (CSK) [42; 43; 44; 45] synchronization schemes have been proposed for encoding and decoding of messages in laser systems. In the CSK scheme, two separated states corresponding to bit sequences (\"1\" and \"0\") of a message are sent to a receiver laser and based on the synchronization between TL and RL, the message is decoded at the receiver [42]. A real data, video signal transmission in chaos communication using the system of semiconductor lasers was demonstrated by [PERSON] et al. [46]. In 2005, a field-based experiment of chaos-based optical communication by CSK scheme of encoding using semiconductor lasers with the optical fiber networks has been demonstrated [4]. In spite of all existing work, to implement secure optical communication in practical use needs extensive studies, for example, improvement in synchronization while allowing parameter mismatch between transmitter and receiver laser, robustness in communications and enhancement of the degree of security [47]. A good message recovery is possible if the synchronization between transmitter and receiver laser is best. In a recent study the synchronization quality is shown to be affected by intra-cavity propagation delay (\(\tau_{PD}\)) in chaotic semiconductor lasers [48; 49].  
In this article, we discuss our numerical investigations on the effect of intra-cavity propagation delay on the message encoding and decoding using uni-directionally coupled semiconductor lasers. Based on the CSK scheme, we encode 1.2 Gbit/s bit rate (BR) message with the chaotic output of the transmitter laser and transmit to receiver laser. The message is decoded at the receiver laser and studied the effect of intra-cavity propagation delay \(\tau_{PD}\) on message recovery. The message recovery quality has been evaluated and characterized by bit error rate (BER) analysis of the recovered message. We have systematically investigated the influence of intra-cavity propagation delay in the message recovery process, by considering various coupling rates, detunings, modulation depths, and bit rates of the encoded message. The BER of the recovered message has been reduced after considering intra-cavity propagation delay correction in the receiver laser system.