Efficient Linear Time Encoding for LDPC Codes

Tomoharu SHIBUYA
Kazuki KOBAYASHI

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A    No.7    pp.1556-1567
Publication Date: 2014/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.1556
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
LDPC codes,  encoding of linear codes,  block triangular matrices,  a system of linear equations,  

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Summary: 
In this paper, we propose a new encoding method applicable to any linear codes over arbitrary finite field whose computational complexity is O(δ*n) where δ* and n denote the maximum column weight of a parity check matrix of a code and the code length, respectively. This means that if a code has a parity check matrix with the constant maximum column weight, such as LDPC codes, it can be encoded with O(n) computation. We also clarify the relation between the proposed method and conventional methods, and compare the computational complexity of those methods. Then we show that the proposed encoding method is much more efficient than the conventional ones.

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