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Design of Efficiently Encodable Rate-Compatible LDPC Codes Using Vandermonde Extension Matrices

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Abstract

A low-complexity algorithm for the design of efficiently-encodable rate-compatible (RC) low-density parity-check (LDPC) codes by deterministically extending an irregular repeat-accumulate (IRA) is introduced. The extending structure is based on circulants shifted according a truncated Vandermonde matrix (VM) and therefore termed as “extended VM” (eVM). The novel extending algorithm is significantly less computationally complex than other known similar methods since it does not require any optimization of the extending profile or any post-construction girth conditioning. To improve the codes’ properties and correcting capabilities in low code rate applications, the optimal proportions of degree-1 and degree-2 parity bits for the extended nodes are investigated and, in contrast to existing deterministic extending approaches for RC-IRA codes, an extending increment step equal to half the information block length is chosen. Various bit error rate (BER) and frame error rate (FER) have been obtained for different code rates, R, and information block length k 0 = 512 and 1024 bits considering an additive white Gaussian noise (AWGN) channel. The results have demonstrated that the proposed eVM RC-LDPC codes, despite their very simple structure and very low computational complexity, exhibit excellent performance only slightly inferior to both dedicated IRA and previously known RC-IRA codes for different data block sizes.

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Authors and Affiliations

  1. Institute for Space Applications and Remote Sensing (ISARS), National Observatory of Athens (NOA), Metaxa and Vas. Pavlou Str, Palaia Penteli, 15236, Athens, Greece

    David Benmayor, Stylianos Papaharalabos, P. Takis Mathiopoulos & Georgia Tsiropoula

  2. School of Electrical and Computer Engineering (ECE), National Technical University of Athens (NTUA), Zographou Campus, 15773, Athens, Greece

    David Benmayor & Philip Constantinou

Authors
  1. David Benmayor
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  2. Stylianos Papaharalabos
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  3. P. Takis Mathiopoulos
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  4. Georgia Tsiropoula
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  5. Philip Constantinou
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Correspondence to David Benmayor.

Additional information

This paper is part of the 03ED554 research project, implemented within the framework of the “Reinforcement Programme of Human Research Manpower” (PENED) and co-financed by National and Community Funds (20% from the Greek Ministry of Development-General Secretariat of Research and Technology and 80% from E.U.- European Social Fund).

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Benmayor, D., Papaharalabos, S., Mathiopoulos, P.T. et al. Design of Efficiently Encodable Rate-Compatible LDPC Codes Using Vandermonde Extension Matrices. Wireless Pers Commun 60, 695–708 (2011). https://doi.org/10.1007/s11277-010-9969-8

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  • DOI: https://doi.org/10.1007/s11277-010-9969-8

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