Design and Construction of Irregular LDPC Codes for Channels with Synchronization Errors: New Aspect of Degree Profiles


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A    No.10    pp.1237-1247
Publication Date: 2020/10/01
Publicized: 2020/04/08
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020EAP1004
Type of Manuscript: PAPER
Category: Coding Theory
synchronization error,  low-density parity-check (LDPC) codes,  code design,  code construction,  

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Over the past two decades, irregular low-density parity-check (LDPC) codes have not been able to decode information corrupted by insertion and deletion (ID) errors without markers. In this paper, we bring to light the existence of irregular LDPC codes that approach the symmetric information rates (SIR) of the channel with ID errors, even without markers. These codes have peculiar shapes in their check-node degree distributions. Specifically, the check-node degrees are scattered and there are degree-2 check nodes. We propose a code construction method based on the progressive edge-growth algorithm tailored for the scattered check-node degree distributions, which enables the SIR-approaching codes to progress in the finite-length regime. Moreover, the SIR-approaching codes demonstrate asymptotic and finite-length performance that outperform the existing counterparts, namely, concatenated coding of irregular LDPC codes with markers and spatially coupled LDPC codes.