Results on Punctured Low-Density Parity-Check Codes and Improved Iterative Decoding Techniques
- 22 January 2007
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 53 (2) , 599-614
- https://doi.org/10.1109/tit.2006.889701
Abstract
This paper first introduces an improved decoding algorithm for low-density parity-check (LDPC) codes over binary-input-output-symmetric memoryless channels. Then some fundamental properties of punctured LDPC codes are presented. It is proved that for any ensemble of LDPC codes, there exists a puncturing threshold. It is then proved that for any rates R1 and R2 satisfying 0121 to R2 resulting in asymptotically good codes for all rates R1lesRlesR2. Specifically, this implies that rates arbitrarily close to one are achievable via puncturing. Bounds on the performance of punctured LDPC codes are also presented. It is also shown that punctured LDPC codes are as good as ordinary LDPC codes. For BEC and arbitrary positive numbers R121 lesRlesR2 is shown. Based on the above observations, a method is proposed to design good punctured LDPC codes over a broad range of rates. Finally, it is shown that the results of this paper may be used for the proof of the existence of the capacity-achieving LDPC codes over binary-input-output-symmetric memoryless channelsKeywords
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