Addendum to "An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices"

In an earlier transactions paper, Rosnes and Ytrehus presented an efficient algorithm for determining all stopping sets of low-density parity-check (LDPC) codes, up to a specified weight, and also gave results for a number of well-known codes including the family of IEEE 802.16e LDPC codes, commonly...

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Bibliographic Details
Published in:IEEE transactions on information theory 2012-01, Vol.58 (1), p.164-171
Main Authors: Rosnes, E., Ytrehus, O., Ambroze, M. A., Tomlinson, M.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Binary erasure channel
branch-and-bound
Coding, codes
Error correction & detection
Exact sciences and technology
exhaustive stopping set enumeration
Hamming weight
IEEE 802.16 Standards
IEEE 802.16e
Indexes
Information theory
Information, signal and communications theory
Iterative decoding
low-density parity-check (LDPC) code
minimum distance
Signal and communications theory
stopping distance
stopping set
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
tree search
Vectors
weight spectrum
WiMAX
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Summary:In an earlier transactions paper, Rosnes and Ytrehus presented an efficient algorithm for determining all stopping sets of low-density parity-check (LDPC) codes, up to a specified weight, and also gave results for a number of well-known codes including the family of IEEE 802.16e LDPC codes, commonly referred to as the WiMax codes. It is the purpose of this short paper to review the algorithm for determining the initial part of the stopping set weight spectrum (which includes the codeword weight spectrum), and to provide some improvements to the algorithm. As a consequence, complete stopping set weight spectra up to weight 32 (for selected IEEE 802.16e LDPC codes) can be provided, while in previous work only stopping set weights up to 28 are reported. In the published standard for the IEEE 802.16e codes there are two methods of construction presented, depending upon the code rate and the code length. We compare the stopping sets of the resulting codes and provide complete stopping set weight spectra (up to five terms) for all IEEE 802.16e LDPC codes using both construction methods.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2171531