The throughput gain obtained by linear network coding （LNC） grows as the generation size increases, while the decoding complexity also grows exponentially. High decoding complexity makes the decoder to be the bottle...The throughput gain obtained by linear network coding （LNC） grows as the generation size increases, while the decoding complexity also grows exponentially. High decoding complexity makes the decoder to be the bottleneck for high speed and large data transmissions. In order to reduce the decoding complexity of network coding, a segment linear network coding （SLNC） scheme is proposed. SLNC provides a general coding structure for the generation-based network coding. By dividing a generation into several segments and restraining the coding coefficients of the symbols within the same segment, SLNC splits a high-rank matrix inversion into several low-rank matrix inversions, therefore reduces the decoding complexity dramatically. In addition, two coefficient selection strategies are proposed for both centrally controlled networks and distributed networks respectively. The theoretical analysis and simulation results prove that SLNC achieves a fairly low decoding complexity at a cost of rarely few extra transmissions.展开更多
Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been invest...Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation of parallel architectures for multi-bit decoding. However, most of the existing works only focus on the Reed-Solomon matrix-based NBPCs and the probability domain-based non-binary polar decoding, which lack flexible structure and have a large computation amount in the decoding process, while little attention has been paid to general non-binary kernel-based NBPCs and Log-Likelihood Ratio (LLR) based decoding methods. In this paper, we consider a scheme of NBPCs with a general structure over GF(2m). Specifically, we pursue a detailed Monte-Carlo simulation implementation to determine the construction for proposed NBPCs. For non-binary polar decoding, an SCL decoding based on LLRs is proposed for NBPCs, which can be implemented with non-binary kernels of arbitrary size. Moreover, we propose a Perfect Polarization-Based SCL (PPB-SCL) algorithm based on LLRs to reduce decoding complexity by deriving a new update function of path metric for NBPCs and eliminating the path splitting process at perfect polarized (i.e., highly reliable) positions. Simulation results show that the bit error rate of the proposed NBPCs significantly outperforms that of BPCs. In addition, the proposed PPB-SCL decoding obtains about a 40% complexity reduction of SCL decoding for NBPCs.展开更多
To improve the error correction performance, an innovative encoding structure with tail-biting for spinal codes is designed. Furthermore, an adaptive forward stack decoding(A-FSD) algorithm with lower complexity for s...To improve the error correction performance, an innovative encoding structure with tail-biting for spinal codes is designed. Furthermore, an adaptive forward stack decoding(A-FSD) algorithm with lower complexity for spinal codes is proposed. In the A-FSD algorithm, a flexible threshold parameter is set by a variable channel state to narrow the scale of nodes accessed. On this basis, a new decoding method of AFSD with early termination(AFSD-ET) is further proposed. The AFSD-ET decoder not only has the ability of dynamically modifying the number of stored nodes, but also adopts the early termination criterion to curtail complexity. The complexity and related parameters are verified through a series of simulations. The simulation results show that the proposed spinal codes with tail-biting and the AFSD-ET decoding algorithms can reduce the complexity and improve the decoding rate without sacrificing correct decoding performance.展开更多
In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-froze...In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-frozen symbols exist,where the frozen bits in these symbols can be used as activecheck bits to facilitate the decoder.The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes,admitting an easily configurable and flexible implementation,which is an obvious advantage over the existing nonbinary polar codes based on ReedSolomon(RS)codes.A low-complexity decoding method is also introduced,in which only more competitive symbols are considered rather than the whole q symbols in the finite field.To support high spectral efficiency,we also present,in addition to the single level coded modulation scheme with field-matched modulation order,a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity.Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency,suggesting a potential application for future ultra-reliable and low-latency communications(URLLC).展开更多
This paper investigates the performance of the method used to reduce the decoding complexity of rateless codes through the deletion of the received symbols with low reliability. In the decoder, the received symbols wh...This paper investigates the performance of the method used to reduce the decoding complexity of rateless codes through the deletion of the received symbols with low reliability. In the decoder, the received symbols whose absolute value of logarithm likelihood ratio （LLR） is lower than the threshold are removed, together with their corresponding edges, and thus not involved in the decoding process. The relationship between the deletion probability and the likelihood ratio deletion threshold is derived. The average mutual information per received symbol is analyzed in the case of deletion. The required number of symbols for the decoder to keep the same performance as regular decoding decreases since the average mutual information per symbol increases with the deletion, thus reducing the decoding complexity. This paper analyzes the reduction of decoding computations and the consequent transmission efficiency loss from the perspective of mutual information. The simulation results of decoding performance are consistent with those of the theoretical analysis, which show that the method can effectively reduce the decoding complexity at the cost of a slight loss of transmission efficiency.展开更多
This paper introduces a family of error correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low complexity soft ...This paper introduces a family of error correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low complexity soft in, soft out decoding rules can be implemented. We present a decoding rule, based on the Max Log APP(MLA) formulation, which requires a total of only 20 addition equivalent operations per information bit per iteration. Simulation of a rate 1/2 concatenated zigzag code with four constituent encoders with interleaver length 65536 yields a bit error rate (BER) and of 10 5 at 0.9 dB and 1.4 dB away from the Shannon limit by optimal (APP) and low cost sub optimal (MLA) decoders, respectively.展开更多
A family of space-time block codes(STBCs)for systems with even transmit antennas and any number of receive antennas is proposed.The new codeword matrix is constructed by concatenating Alamouti space-time codes to form...A family of space-time block codes(STBCs)for systems with even transmit antennas and any number of receive antennas is proposed.The new codeword matrix is constructed by concatenating Alamouti space-time codes to form a block diagonal matrix,and its dimension is equal to the number of transmit antennas.All Alamouti codes in the same codeword matrix have the same information;thus,full transmit diversity can be achieved over fading channels.To improve the spectral efficiency,multi-level modulations such as multi-quadrature amplitude modulation(M-QAM)are employed.The symbol mapping diversity is then exploited between transmissions of the same information from different antennas to improve the bit error rate(BER)performance.The proposed codes outperform the diagonal algebraic space-time(DAST)codes presented by Damen[Damen et al.IEEE Transactions on Information Theory,2002,48(3):628–636]when they have the same spectral efficiency.Also,they outperform the 1/2-rate codes from complex orthogonal design.Moreover,compared to DAST codes,the proposed codes have a low decoding complexity because we only need to perform linear processing to achieve single-symbol maximum-likelihood(ML)decoding.展开更多
A 4×4 64-QAM multiple-input multiple-output （MIMO） detector is presented for the application of an IEEE 802.1 In wireless local area network. The detector is the implementation of a novel adaptive tree search ...A 4×4 64-QAM multiple-input multiple-output （MIMO） detector is presented for the application of an IEEE 802.1 In wireless local area network. The detector is the implementation of a novel adaptive tree search （ATS） algorithm, and multiple ATS cores need to be instantiated to achieve the wideband requirement in the 802.11 n standard. Both the ATS algorithm and the architectural considerations are explained. The latency of the detector is 0.75 μs, and the detector has a gate count of 848 k with a total of 19 parallel ATS cores. Each ATS core runs at 67 MHz. Measurement results show that compared with the floating-point ATS algorithm, the fixed-point imple- mentation achieves a loss of 0.9 dB at a BER of 10^-3.展开更多
基金supported by the National Great Science Specific Project of China (2012ZX03001028)
文摘The throughput gain obtained by linear network coding （LNC） grows as the generation size increases, while the decoding complexity also grows exponentially. High decoding complexity makes the decoder to be the bottleneck for high speed and large data transmissions. In order to reduce the decoding complexity of network coding, a segment linear network coding （SLNC） scheme is proposed. SLNC provides a general coding structure for the generation-based network coding. By dividing a generation into several segments and restraining the coding coefficients of the symbols within the same segment, SLNC splits a high-rank matrix inversion into several low-rank matrix inversions, therefore reduces the decoding complexity dramatically. In addition, two coefficient selection strategies are proposed for both centrally controlled networks and distributed networks respectively. The theoretical analysis and simulation results prove that SLNC achieves a fairly low decoding complexity at a cost of rarely few extra transmissions.
基金supported in part by the National Natural Science Foundation of China under Grant 61401407in part by the Fundamental Research Funds for the Central Universities under Grant CUC2019B067.
文摘Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation of parallel architectures for multi-bit decoding. However, most of the existing works only focus on the Reed-Solomon matrix-based NBPCs and the probability domain-based non-binary polar decoding, which lack flexible structure and have a large computation amount in the decoding process, while little attention has been paid to general non-binary kernel-based NBPCs and Log-Likelihood Ratio (LLR) based decoding methods. In this paper, we consider a scheme of NBPCs with a general structure over GF(2m). Specifically, we pursue a detailed Monte-Carlo simulation implementation to determine the construction for proposed NBPCs. For non-binary polar decoding, an SCL decoding based on LLRs is proposed for NBPCs, which can be implemented with non-binary kernels of arbitrary size. Moreover, we propose a Perfect Polarization-Based SCL (PPB-SCL) algorithm based on LLRs to reduce decoding complexity by deriving a new update function of path metric for NBPCs and eliminating the path splitting process at perfect polarized (i.e., highly reliable) positions. Simulation results show that the bit error rate of the proposed NBPCs significantly outperforms that of BPCs. In addition, the proposed PPB-SCL decoding obtains about a 40% complexity reduction of SCL decoding for NBPCs.
基金supported by the National Natural Science Foundation of China (61701020)the Scientific and Technological Innovation Foundation of Shunde Graduate School,USTB (BK19BF009)。
文摘To improve the error correction performance, an innovative encoding structure with tail-biting for spinal codes is designed. Furthermore, an adaptive forward stack decoding(A-FSD) algorithm with lower complexity for spinal codes is proposed. In the A-FSD algorithm, a flexible threshold parameter is set by a variable channel state to narrow the scale of nodes accessed. On this basis, a new decoding method of AFSD with early termination(AFSD-ET) is further proposed. The AFSD-ET decoder not only has the ability of dynamically modifying the number of stored nodes, but also adopts the early termination criterion to curtail complexity. The complexity and related parameters are verified through a series of simulations. The simulation results show that the proposed spinal codes with tail-biting and the AFSD-ET decoding algorithms can reduce the complexity and improve the decoding rate without sacrificing correct decoding performance.
基金supported in part by the National Key R&D Program of China(2021YFA1000500)by the National Natural Science Foundation of China(62171356).
文摘In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-frozen symbols exist,where the frozen bits in these symbols can be used as activecheck bits to facilitate the decoder.The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes,admitting an easily configurable and flexible implementation,which is an obvious advantage over the existing nonbinary polar codes based on ReedSolomon(RS)codes.A low-complexity decoding method is also introduced,in which only more competitive symbols are considered rather than the whole q symbols in the finite field.To support high spectral efficiency,we also present,in addition to the single level coded modulation scheme with field-matched modulation order,a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity.Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency,suggesting a potential application for future ultra-reliable and low-latency communications(URLLC).
基金supported by the National Natural Science Foundation of China (61471076)the Program for Changjiang Scholars and Innovative Research Team in University (IRT1299)the Special Fund of Chongqing Key Laboratory (CSTC)
文摘This paper investigates the performance of the method used to reduce the decoding complexity of rateless codes through the deletion of the received symbols with low reliability. In the decoder, the received symbols whose absolute value of logarithm likelihood ratio （LLR） is lower than the threshold are removed, together with their corresponding edges, and thus not involved in the decoding process. The relationship between the deletion probability and the likelihood ratio deletion threshold is derived. The average mutual information per received symbol is analyzed in the case of deletion. The required number of symbols for the decoder to keep the same performance as regular decoding decreases since the average mutual information per symbol increases with the deletion, thus reducing the decoding complexity. This paper analyzes the reduction of decoding computations and the consequent transmission efficiency loss from the perspective of mutual information. The simulation results of decoding performance are consistent with those of the theoretical analysis, which show that the method can effectively reduce the decoding complexity at the cost of a slight loss of transmission efficiency.
文摘This paper introduces a family of error correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low complexity soft in, soft out decoding rules can be implemented. We present a decoding rule, based on the Max Log APP(MLA) formulation, which requires a total of only 20 addition equivalent operations per information bit per iteration. Simulation of a rate 1/2 concatenated zigzag code with four constituent encoders with interleaver length 65536 yields a bit error rate (BER) and of 10 5 at 0.9 dB and 1.4 dB away from the Shannon limit by optimal (APP) and low cost sub optimal (MLA) decoders, respectively.
基金This work was supported in part by the National Basic Research Program of China(Grant No.2007CB310603)the Research Fund of National Mobile Communications Research Laboratory,Southeast University(No.2008A05)+1 种基金the National High Technology Research and Development Program of China(Grant No.2007AA01Z2B1)the National Natural Science Foundation of China(Grant No.60802005).
文摘A family of space-time block codes(STBCs)for systems with even transmit antennas and any number of receive antennas is proposed.The new codeword matrix is constructed by concatenating Alamouti space-time codes to form a block diagonal matrix,and its dimension is equal to the number of transmit antennas.All Alamouti codes in the same codeword matrix have the same information;thus,full transmit diversity can be achieved over fading channels.To improve the spectral efficiency,multi-level modulations such as multi-quadrature amplitude modulation(M-QAM)are employed.The symbol mapping diversity is then exploited between transmissions of the same information from different antennas to improve the bit error rate(BER)performance.The proposed codes outperform the diagonal algebraic space-time(DAST)codes presented by Damen[Damen et al.IEEE Transactions on Information Theory,2002,48(3):628–636]when they have the same spectral efficiency.Also,they outperform the 1/2-rate codes from complex orthogonal design.Moreover,compared to DAST codes,the proposed codes have a low decoding complexity because we only need to perform linear processing to achieve single-symbol maximum-likelihood(ML)decoding.
文摘A 4×4 64-QAM multiple-input multiple-output （MIMO） detector is presented for the application of an IEEE 802.1 In wireless local area network. The detector is the implementation of a novel adaptive tree search （ATS） algorithm, and multiple ATS cores need to be instantiated to achieve the wideband requirement in the 802.11 n standard. Both the ATS algorithm and the architectural considerations are explained. The latency of the detector is 0.75 μs, and the detector has a gate count of 848 k with a total of 19 parallel ATS cores. Each ATS core runs at 67 MHz. Measurement results show that compared with the floating-point ATS algorithm, the fixed-point imple- mentation achieves a loss of 0.9 dB at a BER of 10^-3.
