Research :: ECE :: UD


Communication & Signal Processing

Low-density generator matrix codes

Javier Garcia-Frias

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.

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