Redesign of Channel Codes for Joint Source-Channel Coding Systems over One-Dimensional Inter-Symbol-Interference Magnetic Recording Channels  
Ying Sun  
School of Information Science and Engineering, Huaqiao University, Xiamen 361021, China  
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Chen  
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Chen  
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Zhou  
1  
Kedesign of Channel Codes for Joint Source-Channel Coding Systems over One-Dimensional Inter-Symbol-Interference Magnetic Recording Channels. Electronics **2022**, _11_, 3490. [[https://doi.org/10.3390/electronics11213490](https://doi.org/10.3390/electronics11213490)]([https://doi.org/10.3390/electronics11213490](https://doi.org/10.3390/electronics11213490))  
2  
Chen  
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Zhou  
code in MR channels [17; 18]. The optimization schemes of the channel coding and decoding have been proposed in [19; 20; 21] for ISI channels. A novel alternating direction method of multipliers-based decoding method has been derived for LDPC codes over ISI channels in [20], and a novel channel coding autoencoder has been presented for AWGN channels with discrete-time ISI effects in [21]. Moreover, many researchers have endeavored to design good PLDPC codes over one-dimensional inter-symbol-interference (OD-ISI) MR channels and two-dimensional inter-symbol-interference (TD-ISI) MR channels [22; 23; 24; 25; 26; 27; 28]. For example, a new design scheme and three new types of PLDPC codes were proposed for the partial response (PR) channel model in [22]. The design of PLDPC codes which can approach the independent and uniformly distributed (i.u.d.) capacity of PR channels was addressed in [24]. Moreover, a family of rate-compatible PLDPC codes approaching the i.u.d. capacity of ISI channels was produced in [25]. For the TD-ISI MR channel, the design of PLDPC codes and non-binary PLDPC codes were presented in [26; 27]. In particularly, a survey-type of paper [28] provided an introduction to the latest research advancements in PLDPC-code design over MR channels. However, the above-mentioned works for MR channels both aimed at designing channel codes based on separate coding structures, rather than JSCC systems. Considering that the redundancy left by the source encoder can be exploited at the joint source-channel decoder (JSCD) to reduce the bit-error-rate (BER) over AWGN channels, the JSCC system over MR channels also need to be investigated. As is shown in [7], the optimal channel code in separate systems is no longer optimal in joint systems. Therefore, the design for channel codes in the JSCC system over MR channels should be looked into as well. With this motivation, this work mainly investigates the DP-LDPC system over OD-ISI MR channels and proposes a re-design scheme for channel codes of this system. To be more specific, firstly, a three-stage serially concatenated framework of Turbo equalization is proposed in this system. Moreover, to analyze the convergence-performance of the proposed system, the modified joint protograph extrinsic information transfer (M-JPEXIT) algorithm is designed to investigate the mutual information (MI) evolution among the three components. Additionally, by means of the M-JPEXIT algorithm, a re-design scheme for channel codes is put forward to improve the error performance. Both the M-JPEXIT analysis and the BER simulation results indicate the performance improvement of the re-design scheme in the water-fall region. The main contributions of this paper are as follows. 1. To exploit the redundancy left by the source encoder, a new JSCC system with a three-stage serially concatenated framework of Turbo equalization is proposed for OD-ISI MR channels. 2. In order to analyze the asymptotic-performance for the proposed system, a M-JPEXIT algorithm is designed, which investigates the MI evolution among the Bahl-Cocke-Jelinek-Raviv (BCJR) detector, the channel decoder and the source decoder. 3. An optimization algorithm for channel codes is put forward to improve the error performance of the proposed system by means of the M-JPEXIT algorithm, which takes both degree-1 VN and the type-1 connection edge into consideration.