Bahl-Cocke-Jelinek-Raviv Research Articles

Modified Joint Source–Channel Trellises for Transmitting JPEG Images over Wireless Networks

This paper presents a joint source–channel image transmission model based on a modified trellis construction using variable-length and fixed-length codes. The model employs linear block trellis codes and a modified Bahl–Cocke–Jelinek–Raviv algorithm for decoding in the source channel. Additionally, this model utilizes a hierarchical tree and a parity-check matrix to combine the source and channel codes, reducing errors in the decoding process and enabling the decoding of longer sequences without substantial loss of quality.

Convolutional Neural Network-Based Media Noise Prediction and Equalization for TDMR Turbo-Detection With Write/Read TMR

This article considers a turbo-detection system that includes a convolutional neural network (CNN)-based equalizer, a Bahl-Cocke-Jelinek-Raviv (BCJR) trellis detector, a CNN-based media noise predictor (MNP), and a low-density parity-check (LDPC) channel decoder for two-dimensional magnetic recording (TDMR) in the presence of track misregistration (TMR). The input readings are passed to a 2-D partial response (PR) equalizer, which is either linear or CNN-based. The equalized waveforms are inputs to a 2-D BCJR detector, which generates log-likelihood-ratio (LLR) outputs. The CNN MNP is provided with BCJR LLRs to estimate signal-dependent media noise samples and feed them back to the BCJR. A second pass through the BCJR produces LLRs, which are decoded by an LDPC decoder; achieved areal density (AD) is computed from the LDPC code rate. Spatially varying read- and write-TMR models are developed. We investigate the performance of the proposed system on simulated TDMR readback waveforms generated by grain-switching probabilistic (GSP) simulations. We have two types of GSP datasets. Dataset #1 includes two 10 nm bit length (BL) datasets with 18 and 24 nm track pitch (TP). Dataset #2 has 11 nm BL and 15 nm TP. The comparison baseline is a 1-D BCJR detector with pattern-dependent noise prediction (PDNP) and soft intertrack interference (ITI) subtraction, referred to as 1-D PDNP with LLR exchange. The write-TMR and read-TMR are modeled as cross-track-independent downtrack-correlated random processes. In the presence of joint write- and read-TMR, the proposed turbo-detection system achieves 8.34% and 0.70% AD gain over 1-D PDNP with LLR exchange for TP 18 and 24 nm dataset #1, respectively, and is more robust to TMR compared to the baseline.

BNET: A Neural Network Approach for LLR-Based Detection in the Presence of Bursty Impulsive Noise

Ensuring reliable wireless communications is often a major challenge in environments characterized by bursty impulsive noise. Unfortunately, effective receivers adapted to this problem employ recursive techniques that are computationally complex and challenging to implement where computing and battery resources are limited. As a solution, we propose a computationally efficient neural network-based framework to approximate the log-likelihood ratio function produced by the Bahl Cocke Jelinek Raviv (BCJR) algorithm for single-carrier communication systems. The results show that our method can match the BCJR algorithm’s BER performance in many scenarios and even outperform it when some noise model parameters change over time.

An Efficient Application of Turbo Coding for OFDM In-Phase/Quadrature Index Modulation

We present a method to efficiently apply turbo coding to OFDM in-phase/quadrature index modulation (OFDM-IQ-IM) for both cases of presence and absence of puncturing. We show that using the posterior probabilities of turbo-coded bits in the Bahl-Cocke-Jelinek-Raviv (BCJR) decoding algorithm yields the same decoding performance as using the likelihood probabilities of turbo-coded bits. We investigate the difference in error rate between systematic bits and parity check bits of systematic turbo coding and the difference in error rate between index selecting bits (ISBs) and symbol selecting bits (SSBs) of OFDM-IQ-IM. Based on the results, we devise a new bit mapping scheme that can efficiently split turbo-coded bits into ISBs and SSBs in OFDM-IQ-IM. Simulations show that the proposed bit mapping scheme improves the bit error rate (BER) of the turbo-coded 4QAM-based OFDM-IQ-IM approach and that the turbo-coded 4QAM-based OFDM-IQ-IM approach applying the proposed bit mapping scheme outperforms the turbo-coded 4QAM-based OFDM approach in the high signal-to-noise ratio (SNR) region.

Feedback Capacity of Ising Channels With Large Alphabet via Reinforcement Learning

We propose a new method to compute the feedback capacity of unifilar finite state channels (FSCs) with memory using reinforcement learning (RL). The feedback capacity was previously estimated using its formulation as a Markov decision process (MDP) with dynamic programming (DP) algorithms. However, their computational complexity grows exponentially with the channel alphabet size. Therefore, we use RL, and specifically, its ability to parameterize value functions and policies with neural networks, to evaluate numerically the feedback capacity of channels with a large alphabet size. The outcome of the RL algorithm is a numerical lower bound on the feedback capacity, which is used to reveal the structure of the optimal solution. The structure is modeled by a graph-based auxiliary random variable that is utilized to derive an analytic upper bound on the feedback capacity with the duality bound. The capacity computation is concluded by verifying the tightness of the upper bound by testing whether it is Bahl-Cocke-Jelinek-Raviv (BCJR) invariant. We demonstrate this method on the Ising channel with an arbitrary alphabet size. For an alphabet size smaller than or equal to 8, we derive the analytic solution of the capacity. Next, the structure of the numerical solution is used to deduce a simple coding scheme that achieves the feedback capacity and serves as a lower bound for larger alphabets. For an alphabet size greater than 8, we present an upper bound on the feedback capacity. For an asymptotically large alphabet size, we present an asymptotic optimal coding scheme.

Integer programming‐based non‐uniform window decoding schedules for spatially coupled low‐density parity‐check codes

Spatially coupled low-density parity-check (SC-LDPC) codes generally use a window decoding scheme, which is known to yield a near-optimal decoding, compared to full block decoding. Recently, a non-uniform schedule has been proposed to eliminate unnecessary updates of variable nodes within a window: this schedule is generated based on the behaviour of variable node updates analysed by density evolution. Here, the authors present a new non-uniform schedule based on integer programming, whereby the objective functions and constraints are derived from a protograph-based extrinsic information transfer chart. Our design is more flexible than the previous design, because the integer programming-based design allows reduction of update numbers and performance losses through the constraints function, whereas the previous design requires observation of variable node update behaviour. The authors report the performance of their designs of non-uniform schedules in additive white Gaussian noise (AWGN) and inter-symbol interference (ISI) channels. Particularly, in the ISI channel, the authors’ non-uniform schedules are designed with cooperative decoding between a Bahl-Cocke-Jelinek-Raviv (BCJR) detector and an SC-LDPC decoder.

Turbo-Detection for Multilayer Magnetic Recording Using Deep Neural Network-Based Equalizer and Media Noise Predictor

This article considers deep neural network (DNN)-based turbo-detection for multilayer magnetic recording (MLMR), an emerging hard disk drive (HDD) technology that uses vertically stacked magnetic media layers with readers above the top-most layer. The proposed system uses two layers with two upper layer tracks and one lower layer track. The reader signals are processed by convolutional neural networks (CNNs) to separate the upper and lower layer signals and equalize them to 2-D and 1-D partial response (PR) targets, respectively. The upper and lower layer signals feed 2-D and 1-D Bahl–Cocke–Jelinek–Raviv (BCJR) detectors, respectively. The detectors’ soft outputs feed a multilayer CNN-based media noise predictor whose predicted noise outputs are fed back to the BCJR equalizers to reduce their bit error rates (BERs). The BCJR equalizers also interface with low-density parity-check (LDPC) decoders. Additional BER reductions are achieved by sending soft-information from the upper layer BCJR to the lower layer BCJR. Simulations of this turbo-detection system on a two-layer MLMR signal generated by a grain-switching-probabilistic (GSP) media model show density gains of 11.32% over a comparable system with no lower layer and achieve an overall density of 2.6551 terabits per square inch (Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ).

Improved Recording Performance With Writer Design and Joint Learning-Based Neural Network for Heat-Assisted Interlaced Magnetic Recording

Heat-assisted interlaced magnetic recording (HIMR) further increases the areal density with the interlaced track layout architecture compared to conventional heat-assisted magnetic recording. However, besides the 2-D inter-symbol interference (ISI) and thermal jitters, the transition curvatures due to the circular thermal profile cause severe erasures after write and obvious nonlinear distortions of readback signals. This deteriorates the recording performance severely. Especially the degrees of transition curvatures for the low temperature written track (LT) and high temperature written track (HT) are distinct, which makes the correction of transition curvature with only the writer design impossible. Correspondingly, a comprehensive method consisting of writer design and multitrack detection algorithm with joint learning-based neural network (JLNN) is proposed to mitigate the effects of transition curvature and 2-D ISI for both LT and HT of HIMR. First, a designed writer with splitting main poles produces the spatially nonuniform write field along the crosstrack direction to correct the transition curvature of LT. Then the multitrack detection with JLNN and improved Bahl–Cocke–Jelinek–Raviv (BCJR) detector (JLNN-IB) algorithm is studied to further mitigate the effects of residual transition curvatures, thermal jitters, and 2-D ISI for both HT and LT. Specifically, the readback signals of read head array and decoded log-likelihood ratio (LLR) outputted by the low-density parity check (LDPC) decoder are fed into JLNN to obtain the equalized signal and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> probability (AP) of three tracks. Then the equalized signal as well as AP of current track and corresponding soft bit estimations of adjacent tracks are embedded into the branch metrics of improved BCJR detector for data detection, and the LDPC decoder is cascaded for the error correction. The simulation indicates that at the recording density of 2.11 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , the proposed comprehensive writer design and JLNN-IB algorithm provide 9.2 and 9.7 dB signal to noise ratio (SNR) gains compared to the conventional 2-D neural network equalizer and 2-D linear equalizer under the uniform write field and circular thermal profile, respectively.

Detection Scheme With Joint Intertrack Interference and Media Noise Mitigations for Heat Assisted Interlaced Magnetic Recording

Heat assisted interlaced magnetic recording (HIMR) is a promising candidate for the next-generation of magnetic recording technology to further increase the area density beyond 1Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Specifically, the high temperature and low temperature tracks are written in an interlaced order to improve the recording performance. However, the inter-track interference (ITI), inter-symbol interference (ISI) and thermal jitters brought by the increased recording density and Curie temperature variations are severe in HIMR, which degrade the bit error rate (BER) performance obviously. In this study, we propose a multitrack detection scheme with joint intertrack interference and media noise mitigations. Here a multi-task neural network (MTNN) is designed to simultaneously predict ITI pattern and residual media noise, then the 2D variable equalizers corresponding to different ITI patterns are implemented and predicted residual media noises are embedded into the branch metrics of modified Bahl-Cocke-Jelinek-Raviv (BCJR) detector to mitigate ITI and whiten media noise. The simulation demonstrates that the proposed MTNN with variable equalizer and modified BCJR detector (MTNN+VE+MB) algorithm mitigates the ITI and media noise effectively. At the channel bit density of 3.10 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , it provides 2.6 dB signal-to-noise ratio (SNR) gain compared to that of conventional 2D fixed equalizer with pattern dependent noise prediction detector (FE+PDNP) for the low temperature (LT) tracks with 4% Curie temperature variance.

Multitrack Detection With a Two-Dimensional Soft-Transition Assisted Multitask Neural Network for Heat-Assisted Interlaced Magnetic Recording

Heat-assisted interlaced magnetic recording (HIMR) further increases recording density compared to heat-assisted magnetic recording due to the interlaced track layout. However, the smaller circular thermal profile of the top low-temperature-written tracks results in severe transition curvatures, which causes nonlinear distortions of the readback signal and degrades the bit error rate (BER) performance. Moreover, the increased recording density causes severe two-dimensional (2-D) intersymbol interference (ISI) along both down track and cross track directions. To mitigate the effect of nonlinear distortion and 2-D ISI in an HIMR system, we model a 2-D soft-transition, information-assisted, multitask neural network and modified Bahl–Cocke–Jelinek–Raviv (BCJR) detector (2DST-MTNN-MB) algorithm to detect three tracks simultaneously. The readback signal and 2-D soft-transition information are fed into the multitask neural network to obtain equalized signals and soft bit estimates of three tracks simultaneously. Then, the signal of the current track and soft estimates of the side tracks are embedded into the branch metrics of the modified BCJR detector for data detection, and the low-density parity check decoder is cascaded for error correction. The simulation results show that the 2DST-MTNN-MB algorithm provides 5.0 dB signal-to-noise ratio gains with reduced computation complexity compared with a single-track, single-task neural network and one-dimensional BCJR detector algorithm for the low-temperature-written track at channel bit density of 3.51 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , thereby narrowing the gap of BER performance between high- and low-temperature-written tracks.

Deep Neural Network Media Noise Predictor Turbo-Detection System for 1-D and 2-D High-Density Magnetic Recording

This article presents a concatenated Bahl–Cocke–Jelinek–Raviv (BCJR) detector, low-density parity-check (LDPC) decoder, and deep neural network (DNN) architecture for a turbo-detection system for 1-D and 2-D magnetic recording (1DMR and TDMR). The input readings first are fed to a partial response (PR) equalizer. Two types of the equalizer are investigated: a linear filter equalizer with a 1-D/2-D PR target and a convolutional neural network (CNN) PR equalizer that is proposed in this work. The equalized inputs are passed to the BCJR to generate the log-likelihood-ratio (LLR) outputs. We input the BCJR LLRs to a CNN noise predictor to predict the signal-dependent media noise. Two different CNN interfaces with the channel decoder are evaluated for TDMR. Then, the second pass of the BCJR is provided with the estimated media noise, and it feeds its output to the LDPC decoder. The system exchanges LLRs between BCJR, LDPC, and CNN iteratively to achieve higher areal density. The simulation results are performed on a grain flipping probabilistic (GFP) model with 11.4 Teragrains per square inch (Tg/in2). For the GFP data with 18 nm track pitch (TP) and 11 nm bit length (BL), the proposed method for TDMR achieves 27.78% areal density gain over the 1-D pattern-dependent noise prediction (PDNP). The presented BCJR-LDPC-CNN turbo-detection system obtains 3.877 Terabits per square inch (T/bin2) areal density for 11.4 Tg/in2 GFP model data, which is among the highest areal densities reported to date.

Low Complexity Generalized-LDPC Decoder Based on Trellis Splicing

The high reliability short length low-density parity-check (LDPC) codes for Ultra Reliable Low Latency Communication (URLLC) are particularly important to future wireless communication systems. Even though the error floor region performance can be improved by using generalized-LDPC (G-LDPC) decoder, its penalty of increasing complexity can not be ignored. In this letter, we invoke the early stop criterion and the trellis splicing (TS) method to G-LDPC decoder. Hence, a G-LDPC-TS decoder is proposed. The proposed method can effectively reduce the number of variable nodes (VNs) involved in BCJR (Bahl-Cocke-Jelinek-Raviv) decoding of G-LDPC; thus, it yields a lower computational complexity. The results confirm that our G-LDPC-TS decoder can achieve a significant complexity reduction without sacrificing the performance.

Multitrack Detection With 2-D Iterative Soft Estimate Aided Neural Network Equalizer for Heat-Assisted Interlaced Magnetic Recording

Heat-assisted interlaced magnetic recording (HIMR) with interlaced track layout architecture enables the further increased areal density compared to the conventional heat-assisted magnetic recording. However, the severe transition curvatures of low temperature written tracks cause noticeable nonlinear distortions of readback signal, and the 2-D intersymbol interference (ISI), media noise, and thermal jitter also bring the challenges for data recovery. Correspondingly, a multitrack detection scheme with 2-D iterative soft estimate aided neural network equalizer (2D-ISA NNE) is proposed for the HIMR system, which iteratively feeds back the soft estimate of reliable sidetracks’ information (e.g., high temperature written tracks) during the neural network equalization (NNE) of middle track (e.g., low temperature written track). Here, the Bahl–Cocke–Jelinek–Raviv (BCJR) detector and low-density parity-check (LDPC) decoder are utilized for the following data detection and error corrections. Then, the similar ISA NNE is implemented to recover the sidetracks’ data. It is found that the proposed 2D-ISA NNE algorithm mitigates the 2-D ISI and nonlinear distortion more effectively compared to the conventional 2-D linear equalizer (LE) and neural network equalizer (NNE). For HIMR at the channel bit density of 3.51 Tb/in2 and overlapping ratio of 0.46, the proposed 2D-ISA NNE algorithm significantly decreases the bit error rate gap between the low temperature and high temperature written tracks. For the low temperature written track, it provides 3.1 and 4 dB signal-to-noise ratio (SNR) gains compared to the conventional 2-D NNE and 2-D LE, respectively.

Deep Neural Network a Posteriori Probability Detector for Two-Dimensional Magnetic Recording

In two-dimensional magnetic recording (TDMR) channels, intersymbol interference (within and between tracks) and pattern-dependent media noise are impediments to reaching higher areal density. We propose a novel deep neural network (DNN)-based a posteriori probability (APP) detection system with parallel multi-track detection for TDMR channels. The proposed DNN-based APP detector replaces the trellis-based Bahl–Cocke–Jelinek–Raviv (BCJR) or Viterbi algorithm and pattern-dependent noise prediction (PDNP) in a typical TDMR scenario, in which it directly outputs log-likelihood ratios of the coded bits and iteratively exchanges them with a subsequent channel decoder to minimize bit error rate (BER). We investigate three DNN architectures—fully connected DNN, convolutional neural network (CNN), and long short-term memory (LSTM) network. The DNN’s complexity is limited by employing linear partial response (PR) equalizer pre-processing. The best performing DNN architecture, CNN, is selected for iterative decoding with a channel decoder. Simulation results on a grain-flipping-probability (GFP) media model show that all three DNN architectures yield significant BER reductions over a recently proposed 2D-PDNP system and a previously proposed local area influence probabilistic (LAIP)-BCJR system. On a GFP model with 18 nm track pitch and 11.4 Teragrains/in2, the CNN detection system achieves an information areal density of 3.08 Terabits/in2, i.e., a 21.72% density gain over a standard BCJR-based 1D-PDNP; the CNN-based system also has $3\times $ the throughput of 1D-PDNP, yet requires only 1/10th the computer run time.

Tail‐biting in optimal CPM detectors

The maximum a posteriori (MAP) detection of a continuous phase modulation (CPM) signal deploys the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm that utilises the trellis structure of the CPM signal. For optimal results the start as well as the end state must be known to the MAP detector. While the start state is usually the zero state by convention, the end of the trellis must be terminated properly to yield a defined end state. This leads to an overhead, which size is dependent on the particular CPM parameters. To overcome the decrease of spectral efficiency, a tail-biting technique is presented and compared to termination and truncation in a fair comparison regarding spectral efficiency.

Hardware Design of Concatenated Zigzag Hadamard Encoder/Decoder System With High Throughput

Both turbo Hadamard codes and concatenated zigzag Hadamard codes are ultimate-Shannonlimit-approaching channel codes. The former one requires the use of Bahl-Cocke-Jelinek-Raviv (BCJR) in the iterative decoding process, making the decoder structure more complex and limiting its throughput. The latter one, however, does not involve BCJR decoding. Hence its decoder structure can be much simpler and can potentially operate at a much higher throughput. In this paper, we investigate the hardware design of a concatenated zigzag Hadamard encoder/decoder system and implement it onto an FPGA board. We design a decoder capable of decoding multiple codewords at the same time, and the proposed system can operate with a throughput of 1.44 Gbps - an increase of 50% compared with the turbo Hadamard encoder/decoder system. As for the error performance, the encoder/decoder system with a 6-bit quantization achieves a bit error rate of 2 × 10 -5 at E b /N 0 = -0.2 dB.

Deep Neural Network Based Media Noise Predictors for Use in High-Density Magnetic Recording Turbo-Detectors

This article presents a combined Bahl–Cocke–Jelinek–Raviv (BCJR) and deep neural network (DNN) turbo-detection architecture for 1-D hard disk drive (HDD) magnetic recording. Simulated HDD readings based on a grain flipping probabilistic (GFP) model are input to a linear filter equalizer with a 1-D partial response (PR) target. The equalizer output is provided to the BCJR detector in order to minimize the intersymbol interference (ISI) due to the PR mask. The BCJR detector’s log-likelihood-ratio (LLR) outputs (along with the linear equalizer outputs) are then input to the DNN detector, which estimates the signal-dependent media noise. The media noise estimate is then fed back to the BCJR detector in an iterative manner. Several DNN media noise estimation architectures based on fully connected (FC) and convolutional neural networks (CNNs) are investigated. For GFP data at 48 nm track pitch and 11 nm bit length, the CNN-based BCJR-DNN turbo detector reduces the detector bit error rate (BER) by $0.334\times $ and the per bit computational time by $0.731\times $ compared to a BCJR detector that incorporates 1-D pattern-dependent noise prediction (PDNP). The proposed BCJR-DNN turbo detection architecture can be generalized for two-dimensional magnetic recording (TDMR).

ISI/ITI Turbo Equalizer for TDMR Using Trained Local Area Influence Probabilistic Model

In this paper, a local area influence probabilistic (LAIP) detector for estimating magnetic grain interactions with coded data bits in two-dimensional magnetic recording is combined with a 2-D Bahl-Cocke-Jelinek-Raviv (BCJR)-based detector for joint removal of intertrack interference (ITI) and intersymbol interference (ISI). The LAIP detector sends log-likelihood ratio estimates of coded bits and an estimate of the local ISI/ITI convolution mask to a BCJR-based ISI/ITI detector followed by an irregular-repeat-accumulate decoder. Simulation results on a random Voronoi grain media model with ISI and ITI show that the concatenated LAIP/BCJR system, which detects three tracks simultaneously, achieves user information bit areal densities competitive or higher than results reported in a previous paper that employed the LAIP detector alone on a Voronoi grain channel without ISI/ITI. Simulation results on a grain-flipping probability media model based on micromagnetic simulations show that the proposed detector achieves an 11.3% bit error rate reduction compared to a recently proposed system with a 2-D linear equalizer followed by a two-track BCJR detector with 2-D pattern-dependent noise prediction.

Exploiting 2-Dimensional Source Correlation in Channel Decoding with Parameter Estimation

&lt;span&gt;Traditionally, it is assumed that source coding is perfect and therefore, the redundancy of the source encoded bit-stream is zero. However, in reality, this is not the case as the existing source encoders are imperfect and yield residual redundancy at the output. The residual redundancy can be exploited by using Joint Source Channel Coding (JSCC) with Markov chain as the source. In several studies, the statistical knowledge of the sources has been assumed to be perfectly available at the receiver. Although the result was better in terms of the BER performance, practically, the source correlation knowledge were not always available at the receiver and thus, this could affect the reliability of the outcome. The source correlation on all rows and columns of the 2D sources were well exploited by using a modified Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm in the decoder. A parameter estimation technique was used jointly with the decoder to estimate the source correlation knowledge. Hence, this research aims to investigate the parameter estimation for 2D JSCC system which reflects a practical scenario where the source correlation knowledge are not always available. We compare the performance of the proposed joint decoding and estimation technique with the ideal 2D JSCC system with perfect knowledge of the source correlation knowledge. Simulation results reveal that our proposed coding scheme performs very close to the ideal 2D JSCC system.&lt;/span&gt;

Study on the Structure of an Efficient Receiver for Covert Underwater Communication Using Direct Sequence Spread Spectrum

This paper proposes an underwater communication receive model based on the spread spectrum technique in order to provide the characteristic of a low probability of interception. To do this, turbo equalization techniques employing Bahl-Cocke-Jelinek-Raviv (BCJR) decoding to improve performance through repetition are applied to offer excellent performance even at a low signal to noise ratio (SNR) of transmitted signals due to the spread spectrum technique. A turbo equalization model based on RAKE which increase signal power by summing the received signal through the multipath is proposed to compensate distorted data due to multipath channel and the performance improvements were proven by applying the threshold and weighted coefficient in the RAKE receiver model. The model was applied to covert underwater communication in a multi-sensor environment, and the efficiency of the proposed method was proven through underwater experiments.