Discrete Math Seminar Fall 2008
Algebraic constructions of codes using voltage graphs
Christine Kelley, UNL;
Colloquium on Fri Dec 5
Graph-based codes, such as low-density parity-check (LDPC) codes and repeat-accumulate codes, are being widely studied due to their efficient decoding algorithms and remarkable performance on several communication channels. One recent avenue of approach is to construct these codes by first designing small graphs with suitable properties, and then using random lifts of these "protographs" to represent codes.
In this talk, we introduce an algebraic analog of this approach using voltage graphs. After a brief background on LDPC codes, we present a code construction by giving an algebraic method of choosing the permutation voltages so that the resulting codes have good properties. This construction illustrates how simple results from graph theory and algebra may be used to get codes that outperform their random counterparts.