Skip to main content

Density evolution for deterministic generalized product codes on the binary erasure channel at high rates

Publication ,  Internet Publication
Häger, C; Pfister, HD; GraellAmat, A; Brännström, F
July 1, 2017

Generalized product codes (GPCs) are extensions of product codes (PCs), where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed to randomized code ensembles) and analyze the asymptotic performance over the binary erasure channel under iterative decoding. Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, blockwise braided codes, and staircase codes. It is assumed that the component codes can correct a fixed number of erasures and that the length of each component code tends to infinity. We show that this setup is equivalent to studying the behavior of a peeling algorithm applied to a sparse inhomogeneous random graph. Using a convergence result for these graphs, we derive the density evolution equations that characterize the asymptotic decoding performance. As an application, we discuss the design of irregular GPCs, employing a mixture of component codes with different erasure-correcting capabilities.

Duke Scholars

Altmetric Attention Stats
Dimensions Citation Stats

DOI

ISSN

0018-9448

Publication Date

July 1, 2017

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Häger, C., Pfister, H. D., GraellAmat, A., & Brännström, F. (2017). Density evolution for deterministic generalized product codes on the binary erasure channel at high rates. https://doi.org/10.1109/TIT.2017.2689783
Häger, C., H. D. Pfister, A. GraellAmat, and F. Brännström. “Density evolution for deterministic generalized product codes on the binary erasure channel at high rates,” July 1, 2017. https://doi.org/10.1109/TIT.2017.2689783.
Häger, C., et al. Density evolution for deterministic generalized product codes on the binary erasure channel at high rates. 1 July 2017. Scopus, doi:10.1109/TIT.2017.2689783.

DOI

ISSN

0018-9448

Publication Date

July 1, 2017

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing