Verification-based decoding for packet-based LDPC codes over binary symmetric channels

Research on low-density parity-check (LDPC) codes has traditionally been focused on small alphabets. With the development of communication networks and high-speed wireless communication systems, the operation units are normally blocks of bits organized as packets. Packet-based LDPC codes have a great potential to be used in multi-cast and content delivery networks to help achieve reliable communications. To decode packet-based LDPC codes, a verification-based decoding algorithm (VA) has been proposed by Luby and Mitzenmacher for q-ary symmetric channels (q-SC) with large q. However, as a packet-level block code, packet-based LDPC codes are most likely used as outer codes in concatenated coding schemes. Due to the fact that in a typical communication system, an interleaver is employed between the inner encoder and the outer encoder and the output from the inner decoder is normally in a hard-decision form, a binary symmetric channel (BSC) is thereby most proper to model such a scenario. We will show that in contrast to q-SC with large q, when VA is used for BSC, the probability that a packet is falsely verified plays a dominant role in determining system performance. In this dissertation, we propose an enhanced verification-based decoding algorithm (EVA) to improve the verification conditions and significantly reduce the possibility of the false verifications. In contrast to VA, EVA has much better performance over BSC with only moderate computation complexity increase. We also analyze the performance of VA and EVA over BSC. By reformulating VA (EVA) as a message-passing algorithm, a statistical model is proposed to analyze the frame error rate (FER) performance of VA (EVA). Using a recursive method to find the values of the parameters during the iterative process, the proposed model provides a good estimate of FER for the various packet sizes and channel parameters of practical interest.