New results on the pseudoredundancy
Bull. Korean Math. Soc. 2019 Vol. 56, No. 1, 111-130
https://doi.org/10.4134/BKMS.b180141
Published online 2019 Jan 31
Marcus Greferath, Zihui Liu, Xin-Wen Wu, Jens Zumbr\"agel
Aalto University; Beijing Institute of Technology; Indiana University of Pennsylvania; Laboratory for Cryptologic Algorithms
Abstract : The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding minimum pseudoweight equals its minimum Hamming distance. By using the value assignment of Chen and Kl\o ve we present new results on the pseudocodeword redundancy of binary linear codes. In particular, we give several upper bounds on the pseudoredundancies of certain codes with repeated and added coordinates and of certain shortened subcodes. We also investigate several kinds of $k$-dimensional binary codes and compute their exact pseudocodeword redundancy.
Keywords : LDPC codes, fundamental cone, pseudoweight, pseudocodeword redundancy, subcode-complete, value assignment
MSC numbers : 94B05
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