# Ciphered BCH Codes for PAPR Reduction in the OFDM in Underwater Acoustic Channels
## 1 Introduction  
Acoustic signals enable short, medium and long-range data transmission in the underwater channel [1]. Severe multi-path fading, variation in the speed of sound and absorption-based pathloss severely limit the communication bandwidth and make the channel complex. Moreover, the underwater acoustic (UWA) channel is wideband in nature, since the bandwidth is of the order of carrier frequency [2]. This results in a larger delay spread of the channel and causes inter-symbol interference (ISI). Since the propagation speed of sound is quite low compared to radio frequency (RF) signals, even a small motion of the transmitter and receiver in the channel causes Doppler spreading and signal shifts. This complexity of the underwater channel severely limits the transmission data-rates. Consequently, for a better utilization of the limited bandwidth and to increase the data-rate of the system, several multicarrier communication schemes have been suggested in the past two decades [3, 4, 5, 6, 7, 8]. For enabling multicarrier high data-rate acoustic communication, orthogonal frequency division multiplexing (OFDM) has recently gained a great deal of attention in the UWA domain, and several research works have evaluated the performance of OFDM systems for underwater acoustic channels [2, 9, 10, 11]. It is a reliable and well-studied multicarrier technique with the ability to deal with frequency selectivity of the channel and longer delay spreads [12, 13]. Because of the longer duration of the OFDM symbols, it can counter the ISI caused by the severe multipath in the UWA channels. Despite its advantages, one ofthe foremost issues associated with OFDM is the high peak to average power ratio at the transmitter. It is a widely studied topic in the field of RF OFDM [14; 15; 16; 17; 18], whereas computational and bandwidth limitations render it a unique problem in the acoustic domain [19]. A large peak-to-average power ratio (PAPR) value usually results from the constructive overlapping of random symbol phases to create peaks in the time domain. The presence of non-linear power amplifiers at the transmitter side makes it mandatory to reduce the average power of the system, which causes a loss in performance. In-band distortions and spectral spreading are observed when such a signal passes through non-linear devices, such as high-power amplifiers (HPA). Thus, a high peak to average power ratio causes in-band distortions in an OFDM system and further increases the complexity of the implementation of other blocks, such as analog-to-digital (A/D) and digital-to-analog (D/A) convertors [20]. Various techniques have been suggested to reduce the PAPR of OFDM systems including: (1) signal distortion techniques, e.g., clipping and filtering, windowing, companding and peak cancellation; (2) probabilistic techniques, including partial transmit sequences (PTS), selective mapping (SL), tone injection and tone reservation; and (3) schemes based upon coding, such as linear block coding (LBC), Golay sequences and turbo coding [18]. Bose-Chaudhuri-Hocquenghem (BCH) codes have been used in communication systems for error correction to reduce bit error rates [21]. BCH codes are cyclic codes operating on a group of data bits or blocks, rather than individual bits [22]. Due to their ability to fix multiple errors and simplicity in coding and decoding implementations, they find their uses in various applications. The decoding energy consumption of BCH codes is observed to be a linear function of the number of corrected errors \(t\) and the length of codewords [23]. Some of the common codes used in this work and their generator polynomials generated using MATLAB's bchgenpoly() function are mentioned in Table 1.  
\begin{table}
\begin{tabular}{c  
The Vernam cipher was first used by [PERSON] in 1917 to encrypt telegraph messaging [24]; also called the XOR cipher, its biggest advantage is that encryption and decryption are both achieved using the same operation. At the transmitter, the input data is converted into binary and divided into blocks.