Spatially “Mt. Fuji” Coupled LDPC Codes


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A    No.12    pp.2594-2606
Publication Date: 2017/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.2594
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory and Techniques
density evolution,  LDPC codes,  spatially coupled codes,  

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A new type of spatially coupled low density parity check (SCLDPC) code is proposed. This code has two benefits. (1) This code requires less number of iterations to correct the erasures occurring through the binary erasure channel in the waterfall region than that of the usual SCLDPC code. (2) This code has lower error floor than that of the usual SCLDPC code. Proposed code is constructed as a coupled chain of the underlying LDPC codes whose code lengths exponentially increase as the position where the codes exist is close to the middle of the chain. We call our code spatially “Mt. Fuji” coupled LDPC (SFCLDPC) code because the shape of the graph representing the code lengths of underlying LDPC codes at each position looks like Mt. Fuji. By this structure, when the proposed SFCLDPC code and the original SCLDPC code are constructed with the same code rate and the same code length, L (the number of the underlying LDPC codes) of the proposed SFCLDPC code becomes smaller and M (the code lengths of the underlying LDPC codes) of the proposed SFCLDPC code becomes larger than those of the SCLDPC code. These properties of L and M enables the above reduction of the number of iterations and the bit error rate in the error floor region, which are confirmed by the density evolution and computer simulations.