On the Universality of Spatially Coupled LDPC Codes Over Intersymbol Interference Channels
Abstract: In this paper, we derive the exact input/output transfer functions of the optimal a-posteriori probability channel detector for a general ISI channel with erasures. Considering three channel impulse responses of different memory as an example, we compute the BP and MAP thresholds for regular spatially coupled LDPC codes with joint iterative detection and decoding. When we compare the results with the thresholds of ISI channels with Gaussian noise we observe an apparent inconsistency, i.e., a channel which performs better with erasures performs worse with AWGN. We show that this anomaly can be resolved by looking at the thresholds from an entropy perspective. We finally show that with spatial coupling we can achieve the symmetric information rates of different ISI channels using the same code.
- A. J. Felström and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 2181–2191, Jun. 1999.
- M. Lentmaier, A. Sridharan, D. J. Costello, Jr., and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 5274–5289, Oct. 2010.
- B. P. Smith, A. Farhood, A. Hunt, F. R. Kschischang, and J. Lodge, “Staircase codes: FEC for 100 Gb/s OTN,” IEEE/OSA J. Lightw. Technol., vol. 30, no. 1, pp. 110–117, Jan. 2012.
- S. Moloudi, M. Lentmaier, and A. Graell i Amat, “Spatially coupled turbo-like codes,” IEEE Trans. Inf. Theory, vol. 63, no. 10, pp. 6199–6215, 2017.
- S. Kudekar and H. D. Pfister, “The effect of spatial coupling on compressive sensing,” in Proc. Allerton, Monticello, IL, USA, Sept./Oct. 2010, pp. 347–353.
- S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory, vol. 57, no. 2, pp. 803–834, Feb. 2011.
- S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 7761–7813, Dec. 2013.
- P. S. Nguyen, A. Yedla, H. D. Pfister, and K. R. Narayanan, “Threshold saturation of spatially-coupled codes on intersymbol-interference channels,” in Proc.ICC, Ottawa, ON, Canada, June 2012, pp. 2181–2186.
- H. D. Pfister, “On the capacity of finite state channels and the analysis of convolutional accumulate-m codes,” Ph.D. dissertation, Dept. Elect. Eng., UC San Diego, USA, 2003.
- B. M. Kurkoski, P. H. Siegel, and J. K. Wolf, “Exact probability of erasure and a decoding algorithm for convolutional codes on the binary erasure channel,” in Proc. GLOBECOM , San Francisco, CA, USA, Dec. 2003, pp. 1741–1745.
- M. Lentmaier, M. B. S. Tavares, and G. P. Fettweis, “Exact erasure channel density evolution for protograph-based generalized LDPC codes,” in Proc. Int. Symp. Inf. Theory, Seoul, South Korea, June/July 2009, pp. 566–570.
- C. Wang and H. D. Pfister, “Upper bounds on the MAP threshold of iterative decoding systems with erasure noise,” in Proc. . Int. Symp. Turbo Codes & Related Topics, Lausanne, Switzerland, Sept. 2008, pp. 7–12.
- S.-Y. Chung, G. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 db of the shannon limit,” IEEE Communications Letters, vol. 5, no. 2, pp. 58–60, 2001.
- D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug 2006.
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