Quasi cyclic LDPC (QC-LDPC) codes consisting of circulant permutation matrices (CPM-QC-LDPC) are one of the most attractive types of LDPC codes due to their many advantages. In this paper, we mainly do some research on CPM-QC-LDPC codes. We first propose a two-stage decoding scheme mainly based on parity check matrix transform (MT), which can efficiently improve the bit error rate performance. To optimize the tradeoff between hardware implementation complexity and decoding performance, an improved method that combines our proposed MT scheme with the existing CPM-RID decoding scheme is presented. An experiment shows that both schemes can improve the bit error rate (BER) performance. Finally, we show that the MT decoding mechanism can be applied to other types of LDPC codes. We apply the MT scheme to random LDPC codes and show that it can efficiently lower the error floor.

Similar to algebraic decoding schemes, the (23, 12, 7) Golay code can be decoded by applying the step-by-step decoding algorithm. In this work, a modified step-by-step algorithm for decoding the Golay code is presented. Logical analysis yielded a simple rule for directly determining whether a bit in the received word is correct. The computational complexity can be reduced significantly using this scheme.

Information transmission among biological neurons is carried out by a complex series of spike signals. The input inter-spike arrival times at a neuron are believed to carry information which the neurons utilize to carry out a task. In this paper, a new scheme which utilizes the input inter-spike intervals (ISI) for decoding an input spike train is proposed. A spike train consists of a sequence on input spikes with various inter-spike times. This decoding scheme can also be used for neurons which have multiple synaptic inputs but for which each synapse receives a single spike within one input time window. The ISI decoding neural network requires only a few neurons. Example applications show the usefulness of the decoding scheme.

The stage 3/2 decoding scheme, originally suggested by U. Timor, is modified for a Rayleigh fading channel to improve the performance of a fast frequency-hopped multiple access/multilevel frequency shift keying system. When signal-to-noise ratio per bit is 30 dB, the simulation results show that the modified stage 3/2 decoding scheme increases the spectral efficiency by 11% compared to the modified stage 1 decoding scheme at bit error rate of 10-3. Further, the performance comparisons are made between the modified multistage decoding scheme and the diversity combining methods, where the modified stage 3/2 decoding scheme shows better performance.

A modified error correction/detection scheme based on the scheme by Yi and Lee is proposed. Algebraic decoding is used to perform error correction. Error detection is performed by an absolute value test. It is shown that the proposed scheme bridges the performance gap between Yi and Lee's scheme and Forney's optimal scheme.

An error correction/detection decoding scheme of binary Hamming codes is proposed. Error correction is performed by algebraic decoding and then error detection is performed by simple likelihood ratio testing. The proposed scheme reduces the probability of undetected decoding error in comparison with conventional error correction scheme and increases throughjput in comparison with conventional error detection scheme.