Joint Iterative Decoding of Spatially Coupled Low-Density Parity-Check Codes for Position Errors in Racetrack Memories

Ryo SHIBATA  Gou HOSOYA  Hiroyuki YASHIMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2055-2063
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2055
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding theory and techniques
Keyword: 
insertion and deletion errors,  spatially coupled low-density parity-check code,  forward-backward algorithm,  iterative decoding,  

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Summary: 
Racetrack memory (RM) has attracted much attention. In RM, insertion and deletion (ID) errors occur as a result of an unstable reading process and are called position errors. In this paper, we first define a probabilistic channel model of ID errors in RM with multiple read-heads (RHs). Then, we propose a joint iterative decoding algorithm for spatially coupled low-density parity-check (SC-LDPC) codes over such a channel. We investigate the asymptotic behaviors of SC-LDPC codes under the proposed decoding algorithm using density evolution (DE). With DE, we reveal the relationship between the number of RHs and achievable information rates, along with the iterative decoding thresholds. The results show that increasing the number of RHs provides higher decoding performances, although the proposed decoding algorithm requires each codeword bit to be read only once regardless of the number of RHs. Moreover, we show the performance improvement produced by adjusting the order of the SC-LDPC codeword bits in RM.