Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 970126, 10 pages.

Log-Likelihood Ratio Calculation for Iterative Decoding on Rayleigh Fading Channels Using Padé Approximation

Gou Hosoya and Hiroyuki Yashima

Full-text: Open access

Abstract

Approximate calculation of channel log-likelihood ratio (LLR) for wireless channels using Padé approximation is presented. LLR is used as an input of iterative decoding for powerful error-correcting codes such as low-density parity-check (LDPC) codes or turbo codes. Due to the lack of knowledge of the channel state information of a wireless fading channel, such as uncorrelated fiat Rayleigh fading channels, calculations of exact LLR for these channels are quite complicated for a practical implementation. The previous work, an LLR calculation using the Taylor approximation, quickly becomes inaccurate as the channel output leaves some derivative point. This becomes a big problem when higher order modulation scheme is employed. To overcome this problem, a new LLR approximation using Padé approximation, which expresses the original function by a rational form of two polynomials with the same total number of coefficients of the Taylor series and can accelerate the Taylor approximation, is devised. By applying the proposed approximation to the iterative decoding and the LDPC codes with some modulation schemes, we show the effectiveness of the proposed methods by simulation results and analysis based on the density evolution.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 970126, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807678

Digital Object Identifier
doi:10.1155/2013/970126

Mathematical Reviews number (MathSciNet)
MR3094967

Zentralblatt MATH identifier
06950966

Citation

Hosoya, Gou; Yashima, Hiroyuki. Log-Likelihood Ratio Calculation for Iterative Decoding on Rayleigh Fading Channels Using Padé Approximation. J. Appl. Math. 2013, Special Issue (2013), Article ID 970126, 10 pages. doi:10.1155/2013/970126. https://projecteuclid.org/euclid.jam/1394807678


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