A Note on Weight Distributions of Spatially “Mt. Fuji” Coupled LDPC Codes

Yuta NAKAHARA  Toshiyasu MATSUSHIMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2194-2198
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2194
Type of Manuscript: Special Section LETTER (Special Section on Information Theory and Its Applications)
Category: Coding theory and techniques
Keyword: 
spatially coupled LDPC codes,  weight distributions,  error floors,  

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Summary: 
Spatially “Mt. Fuji” coupled (SFC) low density parity check (LDPC) codes are constructed as a chain of block LDPC codes. A difference between the SFC-LDPC codes and the original spatially coupled (SC) LDPC codes is code lengths of the underlying block LDPC codes. The code length of the block LDPC code at the middle of the chain is larger than that at the end of the chain. It is experimentally confirmed that the bit error probability in the error floor region of the SFC-LDPC code is lower than that of the SC-LDPC code whose code length and design rate are the same as those of the SFC-LDPC code. In this letter, we calculate the weight distribution of the SFC-LDPC code and try to explain causes of the low bit error rates of the SFC-LDPC code.