Let Fp be the finite field of p elements with p prime.If A is a subset of Fp and g is an element of F＊p with order ν,then max{｜A ＋ g·A｜,｜A·A｜} （ν/（ν ＋ ｜A｜2） ）1/12｜A｜13/12.
In this paper, an improved low-complexity sum-product decoding algorithm is presented for low-density parity-check （LDPC） codes. In the proposed algorithm, reduction in computational complexity is achieved by utiliz...In this paper, an improved low-complexity sum-product decoding algorithm is presented for low-density parity-check （LDPC） codes. In the proposed algorithm, reduction in computational complexity is achieved by utilizing fast Fourier transform （FFT） with time shift in the check node process. The improvement in the decoding performance is achieved by utilizing an op- timized integer constant in the variable node process. Simulation results show that the proposed algorithm achieves an overall coding gain improvement ranging from 0.04 to 0.46 dB. Moreover, when compared with the sum-product algorithm （SPA）, the proposed decoding algorithm can achieve a reduction of 42%-67% of the total number of arithmetic operations required for the decoding process.展开更多
In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-of...In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.展开更多
The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic rep...The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic representation of transfer functions. To show this we adopt the topological platform for the circuit analysis and use a recently developed Admittance Method (AM) to achieve the Sum of Tree Products (STP), replacing the determinant and cofactors of the Nodal Admittance Matrix (NAM) of the circuit. To construct a transfer function, we start with a given active circuit and convert all its controlled sources and I/O-ports to nullors. Now, with a solid nullor circuit (passive elements and nullors) we first eliminate the passive elements through AM operations. This produces the STPs. Second, the all-nullor circuit is then used to find the signs or the STPs. Finally, the transfer function (in symbolic, if chosen) is obtained from the ratio between the STPs.展开更多
To utilize residual redundancy to reduce the error induced by fading channels and decrease the complexity of the field model to describe the probability structure for residual redundancy, a simplified statistical mode...To utilize residual redundancy to reduce the error induced by fading channels and decrease the complexity of the field model to describe the probability structure for residual redundancy, a simplified statistical model for residual redundancy and a low complexity joint source-channel decoding（JSCD） algorithm are proposed. The complicated residual redundancy in wavelet compressed images is decomposed into several independent 1-D probability check equations composed of Markov chains and it is regarded as a natural channel code with a structure similar to the low density parity check （LDPC） code. A parallel sum-product （SP） and iterative JSCD algorithm is proposed. Simulation results show that the proposed JSCD algorithm can make full use of residual redundancy in different directions to correct errors and improve the peak signal noise ratio （PSNR） of the reconstructed image and reduce the complexity and delay of JSCD. The performance of JSCD is more robust than the traditional separated encoding system with arithmetic coding in the same data rate.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11271249)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120073110059)
文摘Let Fp be the finite field of p elements with p prime.If A is a subset of Fp and g is an element of F＊p with order ν,then max{｜A ＋ g·A｜,｜A·A｜} （ν/（ν ＋ ｜A｜2） ）1/12｜A｜13/12.
文摘In this paper, an improved low-complexity sum-product decoding algorithm is presented for low-density parity-check （LDPC） codes. In the proposed algorithm, reduction in computational complexity is achieved by utilizing fast Fourier transform （FFT） with time shift in the check node process. The improvement in the decoding performance is achieved by utilizing an op- timized integer constant in the variable node process. Simulation results show that the proposed algorithm achieves an overall coding gain improvement ranging from 0.04 to 0.46 dB. Moreover, when compared with the sum-product algorithm （SPA）, the proposed decoding algorithm can achieve a reduction of 42%-67% of the total number of arithmetic operations required for the decoding process.
文摘In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.
文摘The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic representation of transfer functions. To show this we adopt the topological platform for the circuit analysis and use a recently developed Admittance Method (AM) to achieve the Sum of Tree Products (STP), replacing the determinant and cofactors of the Nodal Admittance Matrix (NAM) of the circuit. To construct a transfer function, we start with a given active circuit and convert all its controlled sources and I/O-ports to nullors. Now, with a solid nullor circuit (passive elements and nullors) we first eliminate the passive elements through AM operations. This produces the STPs. Second, the all-nullor circuit is then used to find the signs or the STPs. Finally, the transfer function (in symbolic, if chosen) is obtained from the ratio between the STPs.
文摘To utilize residual redundancy to reduce the error induced by fading channels and decrease the complexity of the field model to describe the probability structure for residual redundancy, a simplified statistical model for residual redundancy and a low complexity joint source-channel decoding（JSCD） algorithm are proposed. The complicated residual redundancy in wavelet compressed images is decomposed into several independent 1-D probability check equations composed of Markov chains and it is regarded as a natural channel code with a structure similar to the low density parity check （LDPC） code. A parallel sum-product （SP） and iterative JSCD algorithm is proposed. Simulation results show that the proposed JSCD algorithm can make full use of residual redundancy in different directions to correct errors and improve the peak signal noise ratio （PSNR） of the reconstructed image and reduce the complexity and delay of JSCD. The performance of JSCD is more robust than the traditional separated encoding system with arithmetic coding in the same data rate.
