Low Density Parity Check Codes

Low density parity check codes

Summary:	Low density parity check (LDPC) codes were introduced along with an iterative probability-based decoding algorithm by Gallager in the early 1960's. These codes were constructed using sparse random parity check matrices and showed promising distance properties. However, they went largely unnoticed until the advent of turbo codes, where they were “rediscovered” by MacKay, who showed that they perform almost as close to capacity as turbo codes. More recently, Richardson and Urbanke have developed irregular LDPC codes that perform even better than turbo codes for very large block lengths (n>10^5) and can come within 0.1 dB of the Shannon capacity.
People:	Valenti, Sun, Zhao, Sehsadri, Vemury
Partners:	Applied Data Trends
Open Problems:	LDPC codes for block fading channels and the relay channel Frame synchronization for LDPC codes (Sun) Joint source-channel decoding of LDPC coded Markov processes (Seshadri)

Links
Prof. Ryan's handwritten notes on LDPC codes
Prof. MacKay's website
Jian Sun's seminar on LDPC codes
Rudy Urbanke's website on irregular LDPC codes
Sae-Young Chung's website on LDPC codes

References (with suggested order to read them)

[Ry04]	W.E. Ryan, “An introduction to LDPC codes,” in CRC Handbook for Coding and Signal Processing for Recoding Systems (B. Vasic, ed.), CRC Press, 2004.
[Ga62]	R.G. Gallager, “Low-density parity-check codes,” IRE Trans. Inform. Theory, vol. 8, pp. 21-28, Jan. 1962.
[MaNe96]	D.J.C. MacKay and R.M. Neal, “Near Shannon limit performance of low density parity check codes,” IEE Electronics Letters, vol. 32, no. 18, pp. 1645-1655, 29th Aug. 1996. Reprinted in Electonics Letters, vol. 33, no. 6, pp. 457-458.
[Ga63]	R.G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: M.I.T. Press, 1963.
[Ma99]	D.J.C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol. 45, pp. 399-431, Mar. 1999. errata.
[Ta81]	R.M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inform. Theory, vol. 27, pp. 533-547, Sept. 1981.
[Fo01]	M.P.C. Fossorier, “Iterative reliability-based decoding of low-density parity check codes,” IEEE J. Select. Areas Commun., vol. 19, pp. 908-917, May 2001.