Math @ Duke

Publications [#319344] of Henry Pfister
Papers Published
 Yedla, A; Jian, YY; Nguyen, PS; Pfister, HD, A simple proof of threshold saturation for coupled vector recursions,
2012 IEEE Information Theory Workshop, ITW 2012
(December, 2012),
pp. 2529, ISBN 9781467302234 [doi]
(last updated on 2018/06/22)
Abstract: Convolutional lowdensity paritycheck (LDPC) codes (or spatiallycoupled codes) have now been shown to achieve capacity on binaryinput memoryless symmetric channels. The principle behind this surprising result is the thresholdsaturation phenomenon, which is defined by the beliefpropagation threshold of the spatiallycoupled ensemble saturating to a fundamental threshold defined by the uncoupled system. Previously, the authors demonstrated that potential functions can be used to provide a simple proof of threshold saturation for coupled scalar recursions. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled vector recursions. The conditions of the theorem are verified for the densityevolution equations of: (i) joint decoding of irregular LDPC codes for a SlepianWolf problem with erasures, (ii) joint decoding of irregular LDPC codes on an erasure multipleaccess channel, and (iii) admissible protograph codes on the BEC. This proves threshold saturation for these systems. © 2012 IEEE.


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