A comparative study on channel coding scheme for underwater acoustic communication

There are various challenges in underwater acoustic communication (UWA) however bit error rate (BER) is considered as the main challenge as it significantly affects the UWA communication. In this paper, different coding schemes such as convolution, turbo, low density parity check (LDPC), and polar coding based on the t-distribution noise channel are investigated, and binary phase-shift keying (BPSK) modulation with a code rate of 1/2 has considered in the evaluation and analyses. The evaluation of these channel coding schemes is performed based on BER, computational complexity as well as latency. The results have shown the outperform of polar coding in UWA over other channel coding schemes as it has lower BER and lower computational complexity.


INTRODUCTION
Under water explorations, subsea resource extractions, pollution monitoring, national defence missions etc. are being critically analysed by underwater acoustic communications (UWAC) and networking technologies. The applications of UWAC have attracted increased interests as the oceans are explored as a sustainable source of food and energy [1], [2]. Communications across shallow seawater channels are characterized by high multipath, high noise level, strong Doppler and other complex random transmission features. These complicate underwater communication (UWC) in terms of reliability and a low data rate compared with wireless communication [3].
Recent research focus on acoustic communications has sought to address issues such as reliability, latency, and bandwidth efficiency, where adaptation to the changing propagation conditions is the main focus [4]. In the systems' designs, the nature of the acoustic propagation forces trade-offs on the various issues depending on the requirements. For instance, reliability is a trade-off for a high data rate while latency is traded for full reliability. Moreover, a low computational complexity is required to achieve a high-speed data rate system. Thus, in channel coding, computational complexity and reliability are compromised with respect to each other depending on the systems' design. Figure 1 demonstrates the trade-off between reliability, latency and computational complexity considered in channel coding techniques. These channel trade-offs and constraints are challenging; however, acoustic channel exhibit peculiar challenges and solutions. This paper considers a user requirement channel coding scheme for UWAC system of lengthy message transmission.  In this work, different channel coding schemes, turbo, convolution, low density parity check (LDPC), and polar codes are considered and evaluated for application in the transmission of lengthy messages (256<K≤1024 bits) with respect to user requirement of complexity, BER and latency performance on the tdistribution of noise channel with binary phase-shift keying (BPSK) of code rate 1/2. Next, section 2 presents the channel model in UWA while section 3 describes the channel coding schemes. The results and analyses are given in section 4 and finally, 5 concludes the research.

CHANNEL MODEL IN UWA
Based on the analysis of the field data measurements in a shallow water, a noise model of the underwater acoustic channel is presented in [5]. The likelihood density function has been proposed for the noise amplitude distribution and the probability functions have been derived in [5], [6]. Hence, for binary signalling of the channel, an expression to the symbol error probability is presented. The noise data collected from a shallow water was also simulated to show the noise effects on the performance of binary signalling system of UWAC. In addition, t-distribution was used to show good fitting of the field measurement analysis of the amplitude of the noise distribution with average degree of freedom of about 3. The (1) expresses the symbol error probability of the binary UWA noise channel.
( ) Where x is a vector of M discrete amplitude levels of noise, and bo / EN is the energy per bit to noise power spectral density ratio. Some researchers have indicated that the noise distribution in shallow water follows the gaussian distribution while others assume the noise distribution in UWA is non-white and non-gaussian [7], [8].

CHANNEL CODING SCHEMES
In channel coding, redundancies are added to some useful bits to secure the data in a noisy channel and to reduce transmission errors to the minimum regardless of its intricacies in communication systems. The main step of the channel coding procedures is partitioning the coding into several subsets. There are four common kinds of the channel coding schemes and these are convolutional codes (CC), turbo codes (TC), polar codes (PC), and LDPC code [9].

Convolution code
Convolution code (CC) is a division of linear error-code broadly applicable to systems such as IS-95 based narrow band CDMA, GSM, and WCDMA [10]. A set number of the shift registers is used to develop the convolutional encoder. Each of the input bits is made to enter the shift register with the encoder output obtained from the combination of the bits in the shift register. Three parameters, the output bits, v, input bits, u and the number of memory registers, m are used to define CC [11]. The code rate, R=u/v gives the coding efficiency with values of u and v ranging from 1 to 8 and 2 to 10, respectively. One CC defined as CC (7,5) was used. Using trellis representation by employing four states following the CC order, viterbi algorithm was utilized for the decoding.
The decoding could be soft or hard. In hard decoding, only binary values are used, but real values, generated by the output equalizer, are utilized in soft decoding. However, sequential decoding comes with a disadvantage of returning a random variable of the searched number of state metrics [12]. The increasing value of the look-ahead length of the feedback decoder not only increase the coding gain but also increases the complexity of the decoding implementation [13]. With the viterbi algorithm, exponential decrease in the error probability with increasing number of code states, S and constraint length, u is its disadvantage. Some research works such as those presented in [14], [15] have utilized CC in underwater acoustic with u-order code implemented by several options. Figure 3 shows the best polynomial, which is arrived at by simulations, and trial and error method [16].

Turbo code
TC are normally comprised of two parallel convolution encoders separated by an interleaver [17]. The main aim is the selection of suitable interleaver by the construction of the polynomial codes for individual encoders. With the considerations of the individual encoders as convolutional, the interleaver is the main element to be analysed and discussed in the encoding process. Figure 4 shows a turbo encoder using an interleaver. A systematic stream output, and a parity stream, 1 are contained in the first encoder (containing the systematic and the first parity stream) while only parity stream, 2 is present in the second individual encoder (containing the interleaved systematic stream and the second parity stream) resulting to the formation of 1/3 TC. In addition, performance losses are avoided by acknowledging the first and last states of the encoder at the decoder by trellis termination. Two soft-input soft-output (SISO) decoders represents the turbo decoder at the decoding unit. It is worthy of note that both turbo decoders and the convolutional decoders are similar in structure with only a few variations. The decoding iterative scheme is essentially comprised of an interleaver, a posteriori probability (APP) decoder and deinterleaver [11]. Figure 4. Turbo code structure [11] Nevertheless, turbo coding is faced with a major challenge of characteristic delay linked with both the decoding algorithm and the interleaver [10]. The associated high implementational complexities could make the block lengths and code rates fail to satisfy the requirements of UWA [18]. Several submissions have been made on turbo codes and its use in UWA [5], [10], [19].

LDPC code
A class of linear error-correction code, LDPC matrix code, was in 1962, introduced by Gallager [20]. It is characterized by a sparsed parity check matrix H. WiMAX and DVB-S2 adopted LDPC code. LDPC code can be considered regular or irregular LDPC codes [21]. It is regular when H has equal number of ones in each column, wc and the equal number of ones in each row, wr [22]. An example of regular binary LDPC codes [21] is the original Gallager codes [20]. Although, it has generally very large size of H matrix, it has very low the density of the nonzero element [12]. LDPC code of length, n can be written as (n, wc, wr). Thus, each information bit is characterized by wc parity checks while each parity check bit is characterized by wr information bits [12]. An algebraic construction can be used to represent the parity check matrix, H [21], and by Tanner graph [21]. In this case, the variable or bit nodes (VN or BN) in Tanner graph is equal to wc, and the check nodes (CN) is equal to wr connected by 1s in the H matrix. The representation of Tanner graph is shown in Figure 5. An example of H matrix algebra representation is given in (2)  LDPC is a simple code which is characterised by linear time encoding and decoding with high efficiency and low complexity compared with turbo code. LDPC code is a high-performance coding scheme of RF communication, however, it is not used in the UWAC. This is because firstly, a long package (about 1,000 bits) is needed whereas the UWA communication commonly adopts a short package since the channel is characterised by variable propagation delay and low communication rate [10]. Secondly, it requires more iterations which makes it more complex as compared to other simplified codes [23].

Polar code
In 2009, PC were invented by Erdal Arikan [24]. This class of linear error-correction code was introduced based on polarization technique, a new concept. PC became active research focus as soon as they were invented. This is owned to the fact that PC demonstrate promising outcome with increasing capacity. They have shown better performance over other coding techniques and hence, extended to cover a number of applications and generalizations as presented in [25]. PC offer very low complexity and explicit construction encoding and decoding. Furthermore, arbitrary design of the code rate of a PC is possible making it more flexible for applications to various scenarios, such as security coding on the physical layer [3]. PC can be defined as (N, K) with N and K denoting the encoded block and the information block lengths, respectively. N=2 n , and n≥0 where n is a natural integer [26]. The remaining N−K indices is called the frozen bit indices [26]. Channel polarization transform is used to construct the PC [27] with the polarization transform being the encoder, which is given by the kernel of (3) [24].
For larger input size, the transform is found the kronecker product of this kernel with itself. This causes the PC to have lengths of powers of 2. For a code of length N, and =log 2 ( ), the encoder is given by (4).

= ⊗
Where n F  F is the Kronecker product of F with itself for n times. The encoding is then carried out as in (4), which is shown in Figure 6 for a code of length 4. In this study, the technique of successive cancellation (SC) decoding is applied as the decoder for the PC due to the regular structure of the PC.

RESULTS AND ANALYSES
This section presents the outcomes of UWA system simulation to evaluate the performance of channel coding schemes based on t-distribution of the noise channel. Table 1 shows the simulation parameters applied for the communication scheme. The analysis of UWA system is evaluated in three phases. Firstly, BER reduction of CC, TC, LDPC and PC is assessed and compared with the signal to noise ratio (SNR). Secondly, the computational complexity level was analysed and lastly, the decoding latency of the channel coding schemes is investigated and discussed. The results of the simulations were retrieved from simulation in MATLAB using the adopted BPSK with code rate 1/2.

BER performance
For UWAC system of message transmission, BER reduction is the first requirement of the channel coding. The reliability is then evaluated based on BER comparison of CC, turbo, LDPC, and PC schemes for the UWAC. This is done for the transmission of different lengths of messages using the parameters as determined in Table 1. The simulations results for all the schemes are depicted in Figures 7-9. These results are compared with the uncoded schemes by theory and simulation for the length of message (256≤K≤1024 bits) at code rate 1/2. Good performance for UWA based on TC, LDPC, and PC are depicted in Figure 7 where the BER of all the schemes is less than 10 -4 for channels with low SNR (0 to 3 dB), which notably outperforms the CC.  Figures 8 and 9, it is clear that polar code scheme is more significant (BER performance is 10 −3 at SNR -1 dB) than TC, LDPC, and CC schemes for different message lengths (512≤K≤1024 bits) at code rate of 1/2. The PC scheme has better reliability with an improvement of 1.5 dB channel gain compared with TC scheme at length [K=512 and 1024 bits] because the SC decoder of polar code has an acceptable performance in short length messages however, it achieves better results in longer length messages. Also, Figures 8 and 9 reveal that BER of 10 −4 at message K=512 and 1024 bits is achievable using the TC. Since the message length is short and TC is characterized by random interleaving, the random position in the medium is not really very random. Furthermore, the decoding capability is limited by punctured TC to correct the errors emanating from the removal of some of the parity bits.

Complexity
The computational complexity is an essential performance metric to be evaluated in codes building and its applied especially in UWA. Therefore, in this paper, the complexity evaluation is analysed and discussed, which is important in examining the computational complexity in the encoding and decoding techniques. In this section, it is required to understand the complexity of the decoding algorithm used to evaluate and find the iteration number identical to providing fair comparison for different schemes. The decoding complexity can be evaluated through multiple mathematical operations such as addition, subtract, multiplication, division, and comparison. Based on code building, different result conclusions can be obtained.
The parameters related to the computational complexity of the PC scheme is calculated and compared with TC, LDPC, and CC schemes. Table 2 presents the equations used in the determination of the number of operations for the various schemes. The parameters K, R, and N denote the information block length, the code rate and the encoded block length respectively [24], [26]. Additionally, m represents the memory length of the component for TC and CC [17], [28]; DC and DV represent the average check degree and average variable degree respectively for LDPC scheme [29], while imax stands for the maximum number of iterations.  [24] ( 2 ( )) Turbo [26] Imax× 16×K×2 m +Imax× 8×K×2 m LDPC [29] Imax× 2×N×dv +M× (2×dc-1)+Imax× M×dc Convolution [28] 4·R·N·2 m Table 3 shows the comparison of the computational complexity of each studied channel coding scheme with TC scheme. It can be seen that the computational complexity of PC scheme is kept lowest as compared with other coding schemes along with the variation of K parameter. This could be attributed that the PC scheme is constructed based on simple algorithm (SC). Therefore, it is implemented efficiently by the factor graph of the code that has a structure resembling the fast fourier transform (FFT) [24]. On the other hand, the coding schemes of TC and LDPC show higher computational complexity compared with PC and CC schemes. This is because, they construct base on an iterative algorithm with high number of iterations leading to increase in the computational complexity. The comparison is clearly illustrated in Figure 10.

Latency
Latency is considered as the third requirement for the implementation of UWA communication channel coding schemes. It is defined as the time taken for the message bits transmitted over all communication blocks as displayed in Figure 2. In this section, the latency is evaluated and compared in terms of different channel decoding schemes such as polar, turbo, LDPC and convolution coding. The MATLAB functions tic and toc are used to calculate the decoding latency time with taking in consideration the type of processor used  Figure 11 is the computational latency of the different channel coding schemes of UWA for transmitted message length of 256≤K≤1024 bits at code rate of 1/2. The PC gives higher decoding computational latency compared with the other coding schemes as a result of the serial decoding by SC algorithm. It is time-consuming and could get worse with an increasing code length, N. Figure 11. Decoding computational latency Figure 11 also shows TC (MAX-Log-MAP) and LDPC (MSP) give have a higher decoding computational latency than CC (viterbi) owing to the associated iterative algorithms. Higher decoding computational latency is given by the LDPC (MSP) compared with the TC (MAX-Log-MAP) since LDPC (MSP) requires more number of iterations (Imax=16) than the TC (Imax=8). However, if the system can tolerate large time delay and complexity, TC will be considered one of the competing error correction codes.

CONCLUSION
In conclusion, different channel coding schemes of convolution, turbo, LDPC, and polar coding were analysed for UWA system based on the t-distribution noise channel with BPSK modulation. The evaluated results of the different coding schemes show that polar coding is the optimum channel coding scheme for UWA as it fulfils user requirements in terms of BER reduction and low computational complexity. Moreover, other requirements such as application type, quality, cost, and data transmission rate are often considered in the choice of channel coding techniques. For instance, the high-speed data rate requires low computational complexity, whereas an excellent BER reduction performance is needed for high-quality. Hence, there is always a trade-off between computational complexity and BER reduction performance in the channel coding techniques. This must be kept firmly considered in the choice of channel coding technique for BER reduction.