Systematic design of low-density parity-check code ensembles for binary erasure channels

Authors:
Hamid Saeedi;Amir H. Banihashemi
Affiliations:
Electrical and Computer Engineering Department, University of Massachusetts, Amherst, MA and Broadband Communications and Wireless Systems Centre, Department of Systems and Computer Engineering, C ...;BCWS Centre, Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada
Venue:
IEEE Transactions on Communications
Year:
2010

Citing 13
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Design of capacity-approaching irregular low-density parity-check codes

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Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation

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Finite-length analysis of low-density parity-check codes on the binary erasure channel

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Capacity-achieving sequences for the erasure channel

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Parity-check density versus performance of binary linear block codes over memoryless symmetric channels

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New sequences of capacity achieving LDPC code ensembles over the binary erasure channel

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Abstract

We propose a systematic method to design irregular low-density parity-check (LDPC) codes for binary erasure channels (BEC). Compared to the existing methods, which are based on the application of asymptotic analysis tools such as density evolution or Extrinsic Information Transfer (EXIT) charts in an optimization process, the proposed method is much simpler and faster. Through a number of examples, we demonstrate that the codes designed by the proposed method perform very closely to the best codes designed by optimization. An important property of the proposed designs is the flexibility to select the number of constituent variable node degrees P. The proposed designs include existing systematic designs as a special case with P = N - 1, where N is the maximum variable node degree. Compared to the existing systematic designs, for a given rate and a given δ 0, the designed ensembles can have a threshold in δ-neighborhood of the capacity upper bound with smaller values of P and N. They can also achieve the capacity of the BEC as N, and correspondingly P and the maximum check node degree tend to infinity.