Fast Adjustable NPN Classification Using Generalized Symmetries

NPN classification of Boolean functions is a powerful technique used in many logic synthesis and technology mapping tools in FPGA design flows. Computing the canonical form of a function is the most common approach of Boolean function classification. In this paper, a novel algorithm for computing NPN canonical form is proposed. By exploiting symmetries under different phase assignments and higher-order symmetries of Boolean functions, the search space of NPN canonical form computation is pruned and the runtime is dramatically reduced. The algorithm can be adjusted to be a slow exact algorithm or a fast heuristic algorithm with lower quality. For exact classification, the proposed algorithm achieves a 30× speedup compared to a state-of-the-art algorithm. For heuristic classification, the proposed algorithm has similar performance as the state-of-the-art algorithm with a possibility to trade runtime for quality

PERFORMANCE COMPARISON OF NON-INTERLEAVED BCH CODES AND INTERLEAVED BCH CODES

This project covers the research about the BCH error correcting codes and the performance of interleaved and non-interleaved BCH codes. Both long and short BCH codes for multimedia communication are examined in an A WGN channel. Algorithm for simulating the BCH codes was also being investigated, which includes generating the parity check matrix, generating the message code in Galois array matrix, encoding the message blocks, modulation and decoding the message blocks. Algorithm for interleaving that includes interleaving message, including burst errors and deinterleaving message is combined with the BCH codes algorithm for simulating the interleaved BCH codes. The performance and feasibility of the coding structure are tested. The performance comparison between interleaved and noninterleaved BCH codes is studied in terms of error performance, channel performance and effect of data rates on the bit error rate (BER). The Berlekamp-Massey Algorithm decoding scheme was implemented. Random integers are generated and encoded with BCH encoder. Burst errors are added before the message is interleaved, then enter modulation and channel simulation. Interleaved message is then compared with noninterleaved message and the error statistics are compared. Initially, certain amount of burst errors is used. "ft is found that the graph does not agree with the theoretical bit error rate (BER) versus signal-to-noise ratio (SNR). When compared between each BCH codeword (i.e. n = 31, n = 63 and n = 127), n = 31 shows the highest BER while n = 127 shows the lowest BER. This happened because of the occurrence of error bursts and also due to error frequency. A reduced size or errors from previous is used in the algorithm. A graph similar to the theoretical BER vs SNR is obtained for both interleaved and non-interleaved BCH codes. It is found that BER of non-interleaved is higher than interleaved BCH codes as SNR increases. These observations show that size of errors influence the effect of interleaving. Simulation time is also studied in terms of block length. It is found that interleaved BCH codes consume longer simulation time compared to non-interleaved BCH codes due to additional algorithm for the interleaved BCH codes

A Comparison Study of LDPC and BCH Codes

The need for efficient and reliable digital data communication systems has been rising rapidly in recent years. There are various reasons that have brought this need for the communication systems, among them are the increase in automatic data processing equipment and the increased need for long range communication. Therefore, the LDPC and BCH codes were developed for achieving more reliable data transmission in communication systems. This project covers the research about the LDPC and BCH error correction codes. Algorithm for simulating both the LDPC and BCH codes were also being investigated, which includes generating the parity check matrix, generating the message code in Galois array matrix, encoding the message bits, modulation and decoding the message bits for LDPC. Matlab software is used for encoding and decoding the codes. The percentage of accuracy for LDPC simulation codes are ranging from 95% to 99%. The results obtained shows that the LDPC codes are more efficient and reliable than the BCH codes coding method of error correction because the LDPC codes had a channel performance very close to the Shannon limit. LDPC codes are a class of linear block codes that are proving to be the best performing forward error correction available. Markets such as broadband wireless and mobile networks operate in noisy environments and need powerful error correction in order to improve reliability and better data rates. Through LDPC and BCH codes, these systems can operate more reliably, efficiently and at higher data rates

Some historical aspects concerning the rise of the first exact measurements of the anomalous magnetic moment of the muon

In this paper, we wish to outline the main historical moments which have led to the first exact measurements of the anomalous magnetic moment of the muon