Iterative Decoding Performance Bounds for LDPC Codes on Noisy Channels

The asymptotic iterative decoding performances of low-density parity-check (LDPC) codes using min-sum (MS) and sum-product (SP) decoding algorithms on memoryless binary-input output-symmetric (MBIOS) channels are analyzed in this paper. For MS decoding, the analysis is done by upper bounding the bit error probability of the root bit of a tree code by the sequence error probability of a subcode of the tree code assuming the transmission of the all-zero codeword. The result is a recursive upper bound on the bit error probability after each iteration. For SP decoding, we derive a recursively determined lower bound on the bit error probability after each iteration. This recursive lower bound recovers the density evolution equation of LDPC codes on the binary erasure channel (BEC) with inequalities satisfied with equalities. A significant implication of this result is that the performance of LDPC codes under SP decoding on the binary erasure channel (BEC) is the best among all MBIOS channe...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Chun-Hao Hsu, Achilleas Anastasopoulos
• Keywords: Binary Erasure Channel, Bit Error Probability, CORR 2006, Education, LDPC Codes