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Because of their capacity-approaching performance and their complexity/latency advantages, spatially-coupled (SC) codes are among the most attractive error-correcting codes for use in modern dense data storage systems. SC codes are constructed by partitioning an underlying block code and coupling the partitioned components. Here, we focus on circulant-based SC codes. Recently, the optimal overlap (OO), circulant power optimizer (CPO) approach was introduced to construct high performance SC codes for additive white Gaussian noise (AWGN) and Flash channels. The OO stage operates on the protograph of the SC code to derive the optimal partitioning that minimizes the number of graphical objects that undermine the performance of SC codes under iterative decoding. Then, the CPO optimizes the circulant powers to further reduce this number. Since the nature of detrimental objects in the graph of a code critically depends on the characteristics of the channel of interest, extending the OO-CPO approach to construct SC codes for channels with intrinsic memory is not a straightforward task. In this paper, we tackle one relevant extension; we construct high performance SC codes for practical 1-D magnetic recording channels, i.e., partial-response (PR) channels. Via combinatorial techniques, we carefully build and solve the optimization problem of the OO partitioning, focusing on the objects of interest in the case of PR channels. Then, we customize the CPO to further reduce the number of these objects in the graph of the code. SC codes designed using the proposed OO-CPO approach for PR channels outperform prior state-of-the-art SC codes by up to around 3 orders of magnitude in frame error rate (FER) and 1.1 dB in signal-to-noise ratio (SNR). More intriguingly, our SC codes outperform structured block codes of the same length and rate by up to around 1.8 orders of magnitude in FER and 0.4 dB in SNR. The performance advantage of SC codes designed using the devised OO-CPO approach over block codes of the same parameters is not only pronounced in the error floor region, but also in the waterfall region. I. INTRODUCTIONAs other data storage systems, magnetic recording (MR) systems operate at very low frame error rate (FER) levels [2]-[5]. Consequently, to ensure high error correction capability in such systems, binary [3], [4], [6] and non-binary (NB) [5], [7]-[10]graph-based codes are used. Under iterative decoding, the objects that dominate the error floor region of low-density paritycheck (LDPC) codes simulated in partial-response (PR) and additive white Gaussian noise (AWGN) systems are different in their combinatorial nature because of the detector-decoder looping and the intrinsic memory in PR systems [5]. In particular, the authors in [5] introduced balanced absorbing sets (BASs) to characterize the detrimental objects in the case of PR (1-D MR) channels. Moreover, the weight consistency matrix (WCM) framework was introduced to systematically remove any type of absorbing sets (ASs) from the graph of an NB-LDPC code [11], [12...

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Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes offer performance advantage over their regular counterparts. In this paper, we present a novel combinatorial framework for designing finite-length irregular SC LDPC codes. Our irregular SC codes have the desirable properties of regular SC codes thanks to their structure while offering significant performance benefits that come with the node degree irregularity. Coding constructions proposed in this work contribute to the existing portfolio of finitelength graph code designs.