This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant...This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.展开更多
Data compression plays a key role in optimizing the use of memory storage space and also reducing latency in data transmission. In this paper, we are interested in lossless compression techniques because their perform...Data compression plays a key role in optimizing the use of memory storage space and also reducing latency in data transmission. In this paper, we are interested in lossless compression techniques because their performance is exploited with lossy compression techniques for images and videos generally using a mixed approach. To achieve our intended objective, which is to study the performance of lossless compression methods, we first carried out a literature review, a summary of which enabled us to select the most relevant, namely the following: arithmetic coding, LZW, Tunstall’s algorithm, RLE, BWT, Huffman coding and Shannon-Fano. Secondly, we designed a purposive text dataset with a repeating pattern in order to test the behavior and effectiveness of the selected compression techniques. Thirdly, we designed the compression algorithms and developed the programs (scripts) in Matlab in order to test their performance. Finally, following the tests conducted on relevant data that we constructed according to a deliberate model, the results show that these methods presented in order of performance are very satisfactory:- LZW- Arithmetic coding- Tunstall algorithm- BWT + RLELikewise, it appears that on the one hand, the performance of certain techniques relative to others is strongly linked to the sequencing and/or recurrence of symbols that make up the message, and on the other hand, to the cumulative time of encoding and decoding.展开更多
基金supported by the National Natural Science Foundation of China under Grants No.61172085,No.61103221,No.61133014,No.11061130539 and No.61021004
文摘This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.
文摘Data compression plays a key role in optimizing the use of memory storage space and also reducing latency in data transmission. In this paper, we are interested in lossless compression techniques because their performance is exploited with lossy compression techniques for images and videos generally using a mixed approach. To achieve our intended objective, which is to study the performance of lossless compression methods, we first carried out a literature review, a summary of which enabled us to select the most relevant, namely the following: arithmetic coding, LZW, Tunstall’s algorithm, RLE, BWT, Huffman coding and Shannon-Fano. Secondly, we designed a purposive text dataset with a repeating pattern in order to test the behavior and effectiveness of the selected compression techniques. Thirdly, we designed the compression algorithms and developed the programs (scripts) in Matlab in order to test their performance. Finally, following the tests conducted on relevant data that we constructed according to a deliberate model, the results show that these methods presented in order of performance are very satisfactory:- LZW- Arithmetic coding- Tunstall algorithm- BWT + RLELikewise, it appears that on the one hand, the performance of certain techniques relative to others is strongly linked to the sequencing and/or recurrence of symbols that make up the message, and on the other hand, to the cumulative time of encoding and decoding.
