Expurgated sphere bound for LDPC

The tightened union bound on the block error probability for low density parity check codes is derived by eliminating the useless codewords out of the union bound. The elimination of these codewords is done by applying Verdu´s theorem and calculating the Hamming weight of the codewords that belong to the irreducible set. By utilizing the similar technique to the conventional sphere bound, we obtain a new tightened sphere bound. This approach is not only simpler than the conventional bound techniques in the sense of computation complexity, but it also extends the reliable region of E_b/N₀ in which the bounds yields meaningful results.