Bulletin of the
Korean Mathematical Society BKMS

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