Construction of Rate-Compatible LDPC Codes Utilizing Information Shortening and Parity Puncturing
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Construction of Rate-Compatible LDPC Codes Utilizing Information Shortening and Parity Puncturing Tao Tian QUALCOMM Incorporated, San Diego, CA 92121, USA Email: [email protected]
Christopher R. Jones Jet Propulsion Laboratory, California Institute of Technology, NASA, CA 91109, USA Email: [email protected] Received 27 January 2005; Revised 25 July 2005; Recommended for Publication by Tongtong Li This paper proposes a method for constructing rate-compatible low-density parity-check (LDPC) codes. The construction considers the problem of optimizing a family of rate-compatible degree distributions as well as the placement of bipartite graph edges. A hybrid approach that combines information shortening and parity puncturing is proposed. Local graph conditioning techniques for the suppression of error floors are also included in the construction methodology. Keywords and phrases: rate compatibility, shortened codes, punctured codes, irregular low-density parity-check codes, density evolution, extrinsic message degree.
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INTRODUCTION
Complexity-constrained systems that undergo variations in link budget may benefit from the adoption of a ratecompatible family of codes. Code symbol puncturing has been widely used to construct rate-compatible convolutional codes [1], parallel concatenated codes [2, 3], and serially concatenated codes [4]. Techniques for implementing rate compatibility in the context of LDPC coding have primarily pursued parity puncturing [5, 6]. In particular, a density evolution model for an additive white Gaussian noise (AWGN) channel with puncturing was developed by Ha et al. [5]. The model was used to find asymptotically optimal puncturing fractions (in a density evolution sense) for each variable node degree of a mother code distribution to achieve given (higher) code rates. Li and Narayanan [7] show that puncturing alone is insufficient for the formation of a sequence of capacity-approaching LDPC codes across a wide range of rates. In addition to puncturing, the authors in [7, 8] used extending (adding columns and rows to the code’s parity matrix) to achieve rate compatibility. In contrast to prior work that has focused primarily on puncturing and extending, this paper proposes a This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
rate-compatible scheme that carefully combines parity puncturing and information shortening. In addition to providing good asymptotic distributions with which to achieve rate compatibility, we also present a column weight assignment strategy that seeks to adhere to the weight distribution goal provided by each rate. The parity puncturing portion of our method leverages the work of Ha et al. [5] while the information shortening part of the approach introduces a novel technique for “fitting” an optimal degree distribution for each component rate to the portion of the graph that effectively implements this rate.
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