Research
Communication & Signal Processing
Low-density generator matrix codes
Javier Garcia-Frias
- Multi-layered schemes in MIMO systems
- OFDM for Cooperative Networks
- Radar Imaging
- 50% Efficient Solar Cells
- Capacity optimization
- Channel coding for non-standard channels with memory
- Exploiting Diversity in Wireless Networks
- Image Compression
- Low-density generator matrix codes
- Message Authentication in Noisy Environments
- Multi-tone blue noise dithering
- Inverse Lithography
- Space-time/frequency coding for MIMO and cooperative communications systems
- Steganalysis of Digital Images and Videos
- Turbo-like codes for distributed source and joint source-channel coding
- Compressive sensing in imaging, sensor networks, and UWB radios
- Lossless Data Compression
Current funding
NSF and ARL/CTA
Group Staff
Participating graduate students
Huiqiong Chai
Inaki Esnaola
Kejing Liu
Hanqing Lou
Ying Zhao
Wei Zhong
Collaborators
Participating collaborators
Luis Castedo (Universidade A Coruna)
In the last decade, helped by the increase in computing power, capacity approaching codes, such as turbo codes and low-density parity check (LDPC) codes, have been proposed. The common characteristics of these codes are their long length and their random-like codeword structure. However, the decoding complexity of turbo codes and the encoding complexity of LDPC codes are substantial. In order to alleviate this problem, we have proposed the use of low-density generator matrix (LDGM) codes, which are a special class of LDPC codes with low encoding and decoding complexity.
Generally speaking, LDGM codes are systematic linear codes with sparse generator matrix. Thus, the encoding procedure is linear and simple, and the parity check matrix (which is also sparse) is easy to calculate due to the systematic structure. The decoding scheme of LDGM codes is similar to that of LDPC codes and based on the representation of code constraints in a graphical manner and the application of belief propagation. Although LDGM codes introduce high error floors, these error floors can be substantially reduced by using parallel or serial concatenation, which leads to a performance comparable to that of traditional LDPC codes.
We are exploring different avenues where the use of LDGM codes leads to improved performance, including MIMO and MAC channels and quantum systems.
Recent publications
F. Vazquez-Araujo, M. Gonzalez-Lopez, L. Castedo, and J. García-Frías, "Design of Serially-Concatenated Low-Density Generator Matrix codes using EXIT Charts", International Symposium on Turbo Codes, April 2006, Munich, Germany.
H. Lou and J. García-Frías, "On the Application of Error-Correcting Codes with Low-Density Generator Matrix over Different Quantum Channels", International Symposium on Turbo Codes, April 2006, Munich, Germany.
W. Zhong and J. García-Frías: "LDGM Codes for Channel Coding and Joint Source Channel Coding of Correlated Sources", EURASIP Journal on Applied Signal Processing, pp. 942-953, May 2005.
