Math @ Duke

Publications [#319351] of Henry Pfister
Papers Published
 Zhang, F; Pfister, HD, Verification decoding of highrate ldpc codes with applications in compressed sensing,
Ieee Transactions on Information Theory, vol. 58 no. 8
(July, 2012),
pp. 50425058 [doi]
(last updated on 2019/07/19)
Abstract: This paper considers the performance of (j,k)regular lowdensity paritycheck (LDPC) codes with messagepassing (MP) decoding algorithms in the highrate regime. In particular, we derive the highrate scaling law for MP decoding of LDPC codes on the binary erasure channel (BEC) and the q ary symmetric channel (qSC). For the BEC and a fixed j, the density evolution (DE) threshold of iterative decoding scales like \Theta (k^{1}) and the critical stopping ratio scales like \Theta (k^{j/(j2)}). For the qSC and a fixed j, the DE threshold of verification decoding depends on the details of the decoder and scales like \Theta (k^{1}) for one decoder. Using the fact that coding over large finite alphabets is very similar to coding over the real numbers, the analysis of verification decoding is also extended to the compressed sensing (CS) of strictly sparse signals. A DEbased approach is used to analyze the CS systems with randomizedreconstruction guarantees. This leads to the result that strictly sparse signals can be reconstructed efficiently with high probability using a constant oversampling ratio (i.e., when the number of measurements scales linearly with the sparsity of the signal). A stoppingsetbased approach is also used to get stronger (e.g., uniforminprobability) reconstruction guarantees. © 19632012 IEEE.


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