# Ciphered BCH Codes for PAPR Reduction in the OFDM in Underwater Acoustic Channels
## 2 Literature Review  
In this section, we detail some of the recent advances in the domain of PAPR reduction and error correcting codes for UWA OFDM systems. Various schemes to reduce PAPR on an OFDM system have been proposed for underwater channels [4; 19; 25; 26; 27; 28; 29; 30] including partial transmit sequences (PTS), low-density parity-check (LDPC) coding, DFT precoding and companding transforms, to name a few. To deal with the high peaks of OFDM modulated systems, [PERSON] and [PERSON] [20] proposed a tone injection technique to reduce the peak to the average power of an underwater acoustic OFDM system. The tones are injected out of the normal transducer bandwidth to minimize the peaks and are added to the system just before D/A conversion. These tones are subsequently filtered out after the signal has passed through the power amplifier before transmitting the final signal. This filtering is an additional process that is required for tone suppression. Multiple techniques have been proposed by [PERSON] and [PERSON] for the optimal placement of the chosen tones, including a random search technique based on limited selection from a set of sequences, as an exhaustive search is not feasible. A PAPR reduction of approximately 0.5 dB to a maximum of 2.5 dB takes place based upon whether the tones have been injected above or below the useful bandwidth and how far the tones are from the useful bandwidth. The data-rate is unaffected in this scheme as there are no overheads. The authors of [31] proposed orthogonal signal division multiplexing (OSDM) for underwater acoustic communication due to its enhanced PAPR reduction performance. However, the complexity of the direct channel equalizer is quite high. An indexed modulated OFDM scheme is proposed in [32], with a PAPR improvement of up to 7 dB over traditional systems. Historically, various implementations, such as [33; 34; 35; 36], have explored block coding techniques to reduce the PAPR of OFDM systems for radio channels. [PERSON], [PERSON], and [PERSON] explored block coding for PAPR reduction in OFDM systems [37]. Input data is organized into blocks, and for each block a code with the lowest PAPR is chosen from a list of selected code words. However, they require exhaustive search and lookup tables incurring heavy processing costs. [PERSON] and [PERSON] [38] analyzed the performance of a PAPR reduction technique based on linear block codes and weighting functions for an OFDM system. The codes are chosen according to the number of subcarriers used, e.g., Hamming (\(7A\)) for an 8-subcarrier system. While the resulting coded words are not in powers of two, a redundant bit is added for easy inverse fast Fourier transform (IFFT) implementation. If the number of sub-carriers used in an OFDM system are \(N\), we use the fundamental principles of [37; 38] while employing \(\mathrm{BCH}(n,k)\) codes to perform an offline exhaustive search for lower orders of \(k\) and random selection sets in the case of higher orders of \(k\), to come up with a single key vector of \((N-1)\) bits that results in the lowest PAPR values for most of the combinations. [PERSON] and [PERSON] employed quadrature phase shift keying (QPSK) signals encoded using BCH(64,10) in a low-complexity channel estimation technique for underwater acoustic MIMO OFDM systems [39]. [PERSON] et al. evaluated various error correcting coding schemes for an underwater OFDM system [40]. The short-length codes evaluated were convolutional, turbo and BCH codes. Simulations using Bellhop [41] and real sea test results demonstrated that the BCH codes had the best overall error correction performance for acoustic OFDM in underwater channels. Additive ciphers [42] work by adding a sequence of \(k\) bits to an input sequence \(m\) to obtain a ciphered sequence \(c\). [PERSON] and [PERSON] [43] compared the performance of the XOR cipher and the phase cipher for an OFDM system. The encryption was performed both before channel coding and after channel coding.