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Using binary images of non binary LDPC codes to improve overall performance

Charly Poulliat, M.P.C. Fossorier, David Declercq

Published Apr 3, 2006• 24 citations
OpenAlex

Abstract

In this paper, we address the problem of the optimization of non binary LDPC codes for finite lengths. Using the binary image of the code, we provide a method for both waterfall and error floor improvements based on the algebraic properties of rows, cycles and stopping sets.

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We investigate the reasons behind the superior performance of belief propagation decoding of non- binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over the binary image has lower complexity, it has worse performance owing to its larger number of stopping sets relative to the original non-binary code. We propose a method to find redundant parity-checks of the binary image that eliminate these additional stopping sets, so that we achieve performance comparable to that of the original non-binary LDPC code with lower decoding complexity.

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Abstract—We investigate the reasons behind the superior performance of belief propagation decoding of non-binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over the binary image has lower complexity, it has worse performance owing to its larger number of stopping sets relative to the original non-binary code. We propose a method to find redundant parity-checks of the binary image that eliminate these additional stopping sets, so that we achieve performance comparable to that of the original non-binary LDPC code with lower decoding complexity. I.

•Oct 11, 2013•2 citations
Abstract — In this paper, a method to design regular (2, dc)-LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes. Index Terms — channel coding, error correction coding, nonbinary LDPC codes, iterative decoding, binary image. I.
In this paper, we use the class of non-binary hybrid LDPC codes to design very efficient low rate codes. To this end, we consider both asymptotic and finite length designs. First, we present an asymptotic analysis to design hybrid LDPC codes distributions and we explicit the cases when it is useful to use it. Then, by optimizing the algebraic properties of some topologies related to the Tanner graph, we design finite length codes. These codes show significant performance improvements both in the waterfall and in the error floor regions, in comparison with existing state-of-the-art low rate coding schemes, like turbo Hadamard or parallel concatenated Zigzag Hadamard codes, and with no increase of complexity. In particular, the minimum distance of low rate hybrid LDPC codes is by far greater than the ones of previously mentioned codes.
In this paper, a method to design regular (2, dc)- LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes.
We investigate the reasons behind the superior performance of belief propagation decoding of non- binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over the binary image has lower complexity, it has worse performance owing to its larger number of stopping sets relative to the original non-binary code. We propose a method to find redundant parity-checks of the binary image that eliminate these additional stopping sets, so that we achieve performance comparable to that of the original non-binary LDPC code with lower decoding complexity.
Abstract—We investigate the reasons behind the superior performance of belief propagation decoding of non-binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over the binary image has lower complexity, it has worse performance owing to its larger number of stopping sets relative to the original non-binary code. We propose a method to find redundant parity-checks of the binary image that eliminate these additional stopping sets, so that we achieve performance comparable to that of the original non-binary LDPC code with lower decoding complexity. I.