Further Results on the Minimum and Stopping Distances of Full-Length RS-LDPC Codes

Haiyang LIU  Hao ZHANG  Lianrong MA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.2   pp.738-742
Publication Date: 2017/02/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Coding Theory
low-density parity-check (LDPC) codes,  RS-LDPC codes,  minimum distance,  stopping distance,  

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Based on the codewords of the [q,2,q-1] extended Reed-Solomon (RS) code over the finite field Fq, we can construct a regular binary γq×q2 matrix H(γ,q), where q is a power of 2 and γ≤q. The matrix H(γ,q) defines a regular low-density parity-check (LDPC) code C(γ,q), called a full-length RS-LDPC code. Using some analytical methods, we completely determine the values of s(H(4,q)), s(H(5,q)), and d(C(5,q)) in this letter, where s(H(γ,q)) and d(C(γ,q)) are the stopping distance of H(γ,q) and the minimum distance of C(γ,q), respectively.