IEEE TRANSACTIONS ON EDUCATION, AUGUST 1970 CONCLUSION The program was written in FORTRAN II to f... more IEEE TRANSACTIONS ON EDUCATION, AUGUST 1970 CONCLUSION The program was written in FORTRAN II to fit a CDC 8090 computer with an 8K memory. The limited storage made it necessary to compress operations and eliminate all steps not absolutely necessary. The printout reflects the necessity to conserve. Various error conditions caused by zero coefficients in the numerator or denominator polynomials were eliminated by patching parts of the program. The two examples were selected partly to illustrate this. All other test input values used gave known correct
In this letter, we present a moment generating function (MGF) based performance analysis of gener... more In this letter, we present a moment generating function (MGF) based performance analysis of generalized selection combining (GSC) receivers operating over independent and identically distributed (i.i.d.) K fading channels. Analytical expressions for the marginal MGF of the signal-to-noise ratio of a single diversity branch for integer plus one-half values of the fading parameter are obtained and used to efficiently evaluate
ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing
This paper demonstrates that the LMS adaptive line enhancer (ALE) can be used to enhance estimati... more This paper demonstrates that the LMS adaptive line enhancer (ALE) can be used to enhance estimation-performance in situations where source signal spectra have tonal components. Time delay estimation obtained by using ALE's as pre-filters followed by a cross correlator (ALE-CC) achieve better performance than the smoothed coherence transform (SCOT) when tonals are present while achieving the basic cross-correlation performance in
2004 IEEE International Conference on Acoustics, Speech, and Signal Processing
The Bell-Labs Layered Space-time (BLAST) architecture is a simple and efficient multi-antenna cod... more The Bell-Labs Layered Space-time (BLAST) architecture is a simple and efficient multi-antenna coding structure that can achieve high-spectral efficiency [1]. Many BLAST detectors require more receiver antennas than transmitter antennas. We propose a novel turbo-processing BLAST detector based on a group detection strategy that can operate in systems with fewer receiver antennas than transmitter antennas. A maximum a posteriori (MAP) decision is made using a group of transmitted symbols and the remaining signal contribution is treated as interference. The interference is characterized as non-zero mean colored noise source that is whitened before a decision is made. The proposed detector, the Group MAP (GMAP) detector, is a generalization of both the MAP detector and the turbo-processing Minimum Mean Squared Error (MMSE) detector in [2, 3]. A novel grouping algorithm is proposed for the GMAP detector. Simulation is used to compare the GMAP detector with the MAP detector and MMSE detector.
Nyquist's third criterion for distortionless trasmission is that the area under the system re... more Nyquist's third criterion for distortionless trasmission is that the area under the system response during a unit interval should be propotional to the signal value. It is shown here that for a system characteristic F(ω) to satisfy this criterion, F(w) multiplied by [(sin ωT/2)/(ωT/2)] should satisfy Nyquist's first criterion.
Due to the unique characteristics of sensor devices, finding the energy-efficient modulation with... more Due to the unique characteristics of sensor devices, finding the energy-efficient modulation with a lowcomplexity implementation (refereed to as green modulation) poses significant challenges in the physical layer design of Wireless Sensor Networks (WSNs). Toward this goal, we present an in-depth analysis on the energy efficiency of various modulation schemes using realistic models in the IEEE 802.15.4 standard to find the optimum distance-based scheme in a WSN over Rayleigh and Rician fading channels with path-loss. We describe a proactive system model according to a flexible duty-cycling mechanism utilized in practical sensor apparatus. The present analysis includes the effect of the channel bandwidth and the active mode duration on the energy consumption of popular modulation designs. Path-loss exponent and DC-DC converter efficiency are also taken into consideration. In considering the energy efficiency and complexity, it is demonstrated that among various sinusoidal carrier-based modulations, the optimized Non-Coherent M-ary Frequency Shift Keying (NC-MFSK) is the most energy-efficient scheme in sparse WSNs for each value of the path-loss exponent, where the optimization is performed over the modulation parameters. In addition, we show that the On-Off Keying (OOK) displays a significant energy saving as compared to the optimized NC-MFSK in dense WSNs with small values of path-loss exponent.
IEEE Transactions on Wireless Communications, 2005
The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with... more The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with postdetection equal gain combining (EGC) over generalized fading channels is of great theoretical interest and practical importance. In this paper, by using a decision variable-based moment generating function approach, exact error probability results for DAPSK over generalized Rician and Nakagami fading channels are derived, taking into account the effects of all the system and fading channel parameters. Several maximum likelihood (ML)-based detectors that do not require channel state information (CSI) are proposed for generalized Rician fading channels, and an exact bit error probability (BEP) union bound for the ML detection is derived. Assuming CSI, a performance upper bound for DAPSK with EGC is also presented. Simulation and numerical results show when both detectors have no CSI, the conventional DAPSK detector may perform closely to (though worse than) the ML detector. However, the EGC receiver with CSI performs substantially better than the ML detector without CSI, and very closely to the coherent APSK detector.
IEEE Transactions on Wireless Communications, 2007
ABSTRACT Multiple-input multiple-output (MIMO) system using orthogonal frequency division multipl... more ABSTRACT Multiple-input multiple-output (MIMO) system using orthogonal frequency division multiplexing (OFDM) technique has become a promising method for reliable high data-rate wireless transmission system in which the channel is dispersive in both time and frequency domains. Due to multiple cochannel interferences in a MIMO system, the accuracy of channel estimation is a vital factor for proper receiver design in order to realize the full potential performance of the MIMO-OFDM system. A robust and improved channel estimation algorithm is proposed in this paper for MIMO-OFDM systems based on the least squares (LS) algorithm. The proposed algorithm, called improved LS (ILS), employs the noise correlation in order to reduce the variance of the LS estimation error by estimating and suppressing the noise in signal subspace. The performance of the ILS channel estimation algorithm is robust to the number of antennas in transmit and receive sides. The new algorithm attains a significant improvement in performance in comparison with that of the regular LS estimator. Also, with respect to mean square error criterion and without using channel statistics, the ILS algorithm achieves a performance very close to that of the minimum mean square error (MMSE) estimator in terms of the parameters used in practical MIMO-OFDM systems. A modification of the ILS algorithm, called modified ILS (MILS), is proposed based on using the second order statistical parameters of channel. Analytically, it is shown that the MILS estimator achieves the exact performance of the MMSE estimator. Due to no specific data sequences being required to perform the estimation, in addition to the training mode, the proposed channel estimation algorithms can also be extended and used in the tracking mode with decision-aided method.
IEEE Transactions on Wireless Communications, 2010
Abstract In this letter, a design metric of the interleaver is derived from the union bound of th... more Abstract In this letter, a design metric of the interleaver is derived from the union bound of the bit error rate (BER) of linearly precoded orthogonal frequency division multiplexing (OFDM) systems, assuming that the power-delay profile of the channel is known at the transmitter. A new cyclic shift interleaving scheme is proposed to improve the BER performance of OFDM systems. The proposed interleaving scheme is parameterized, and it incorporates existing interleaving schemes. The simulation results indicate that the proposed interleavers ...
Abstract This paper develops a family of irregular convolutional codes for bit-interleaved coded ... more Abstract This paper develops a family of irregular convolutional codes for bit-interleaved coded modulation (BICM) systems under iterative detection and decoding. Irregular convolutional codes are constructed through irregular puncturing over multiple mother codes of different memory. Strategies based on fixed-and variable-size trellises are proposed to connect different memory mother codes. The use of irregular puncturing and code memory yields improved coding efficiency with the aid of extrinsic information ...
This paper presents an in-depth analysis on the energy efficiency of Luby Transform (LT) codes wi... more This paper presents an in-depth analysis on the energy efficiency of Luby Transform (LT) codes with Frequency Shift Keying (FSK) modulation in a Wireless Sensor Network (WSN) over Rayleigh fading channels with path-loss. We describe a proactive system model according to a flexible duty-cycling mechanism utilized in practical sensor apparatus. The present analysis is based on realistic parameters including the effect of channel bandwidth used in the IEEE 802.15.4 standard, active mode duration and computation energy. A comprehensive analysis, supported by some simulation studies on the probability mass function of the LT code rate and coding gain, shows that among uncoded FSK and various classical channel coding schemes, the optimized LT coded FSK is the most energyefficient scheme for distance d greater than the predetermined threshold level dT , where the optimization is performed over coding and modulation parameters. In addition, although the optimized uncoded FSK outperforms coded schemes for d < dT , the energy gap between LT coded and uncoded FSK is negligible for d < dT compared to the other coded schemes. These results come from the flexibility of the LT code to adjust its rate to suit instantaneous channel conditions, and suggest that LT codes are beneficial in practical low-power WSNs with dynamic position sensor nodes.
Abstract We consider a scenario where n collaborating cognitive radios (CRs) try to jointly detec... more Abstract We consider a scenario where n collaborating cognitive radios (CRs) try to jointly detect spectrum opportunities in a wide-band spectrum within a predefined spectrum sensing interval T S. We assume that each CR is equipped with a tunable bandpass filter (BPF) and is able to sense one frequency band (channel) at a time. The sensing interval consists of L sensing slots of length T. During each sensing slot, each of the collaborating CRs is assigned to sense one of the channels and report its observation to the other CRs. ...
Tables are presented of good ternary and quaternary codes and they are used in the construction o... more Tables are presented of good ternary and quaternary codes and they are used in the construction of dense sphere packings. Results include 1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50, 2) a class of optimal [ n , 21 codes over GF(q), 3) the (U + U + w I2u + U I U) construction, a new ternary code construction technique that can be used to construct the ternary Reed-Muller codes (and others), and 4) tables of linear ternary and quaternary codes obtained by modifying and combining various codes discovered here and in the literature. Using these codes and a sphere-packing construction, packings are generated in even dimensions up to 100. In dimensions 36 and 60, new record densities appear to have been achieved.
A partial ordering on general finite-state Markov channels is given, which orders the channels in... more A partial ordering on general finite-state Markov channels is given, which orders the channels in terms of probability of symbol error under iterative estimation decoding of a low-density parity-check (LDPC) code. This result is intended to mitigate the complexity of characterizing the performance of general finite-state Markov channels, which is difficult due to the large parameter space of this class of channel. An analysis tool, originally developed for the Gilbert-Elliott channel, is extended and generalized to general finite-state Markov channels. In doing so, an operator is introduced for combining finite-state Markov channels to create channels with larger state alphabets, which are then subject to the partial ordering. As a result, the probability of symbol error performance of finite-state Markov channels with different numbers of states and wide ranges of parameters can be directly compared. Several examples illustrating the use of the techniques are provided, focusing on binary finite-state Markov channels and Gaussian finite-state Markov channels. Furthermore, this result is used to order Gilbert-Elliott channels with different marginal state probabilities, which was left as an open problem by previous work. Index Terms-Estimation-decoding, iterative decoding, lowdensity parity-check (LDPC) codes, Markov channels, partial ordering. I. INTRODUCTION F INITE-STATE Markov channels are binary-input channels, each with a hidden channel state sequence that is generated by a finite-state Markov chain, where the state of the Markov chain determines the instantaneous behavior of the channel. (Throughout this paper, we will take the finite-state nature of the channel to be implicit, and simply refer to Markov channels.) These channels have many applications, such as approximating wireless channels with slow fading, or modeling other correlated noise effects. Capacity and coding for these channels was discussed in [1]. A low-density parity-check (LDPC) code is a type of block code with a very sparse parity-check matrix [2]. Using the sum-product algorithm (SPA) [3] for decoding, it is well
We consider a Code Division Multiple Access (CDMA) cellular network and propose sub-optimal multi... more We consider a Code Division Multiple Access (CDMA) cellular network and propose sub-optimal multiuser detectors which exploit a type of diversity inherent in the system and are based on the processing of signals received at multiple base stations. We investigate the performance of conventional matched-lter, linear, and decisionbased detection schemes, using this diversity scheme, for both synchronous and asynchronous systems. The detection of user signals is based on tracking the signals at several base stations. The optimal detector would operate on all the signals received at all the base stations but would have a high degree of complexity. We discuss the case where the detection of a given signal is based on received signals at a small subset of base stations. We show that with judicious selection of this smaller set of base stations, good performance can be obtained without much increase in complexity.
IEEE TRANSACTIONS ON EDUCATION, AUGUST 1970 CONCLUSION The program was written in FORTRAN II to f... more IEEE TRANSACTIONS ON EDUCATION, AUGUST 1970 CONCLUSION The program was written in FORTRAN II to fit a CDC 8090 computer with an 8K memory. The limited storage made it necessary to compress operations and eliminate all steps not absolutely necessary. The printout reflects the necessity to conserve. Various error conditions caused by zero coefficients in the numerator or denominator polynomials were eliminated by patching parts of the program. The two examples were selected partly to illustrate this. All other test input values used gave known correct
In this letter, we present a moment generating function (MGF) based performance analysis of gener... more In this letter, we present a moment generating function (MGF) based performance analysis of generalized selection combining (GSC) receivers operating over independent and identically distributed (i.i.d.) K fading channels. Analytical expressions for the marginal MGF of the signal-to-noise ratio of a single diversity branch for integer plus one-half values of the fading parameter are obtained and used to efficiently evaluate
ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing
This paper demonstrates that the LMS adaptive line enhancer (ALE) can be used to enhance estimati... more This paper demonstrates that the LMS adaptive line enhancer (ALE) can be used to enhance estimation-performance in situations where source signal spectra have tonal components. Time delay estimation obtained by using ALE's as pre-filters followed by a cross correlator (ALE-CC) achieve better performance than the smoothed coherence transform (SCOT) when tonals are present while achieving the basic cross-correlation performance in
2004 IEEE International Conference on Acoustics, Speech, and Signal Processing
The Bell-Labs Layered Space-time (BLAST) architecture is a simple and efficient multi-antenna cod... more The Bell-Labs Layered Space-time (BLAST) architecture is a simple and efficient multi-antenna coding structure that can achieve high-spectral efficiency [1]. Many BLAST detectors require more receiver antennas than transmitter antennas. We propose a novel turbo-processing BLAST detector based on a group detection strategy that can operate in systems with fewer receiver antennas than transmitter antennas. A maximum a posteriori (MAP) decision is made using a group of transmitted symbols and the remaining signal contribution is treated as interference. The interference is characterized as non-zero mean colored noise source that is whitened before a decision is made. The proposed detector, the Group MAP (GMAP) detector, is a generalization of both the MAP detector and the turbo-processing Minimum Mean Squared Error (MMSE) detector in [2, 3]. A novel grouping algorithm is proposed for the GMAP detector. Simulation is used to compare the GMAP detector with the MAP detector and MMSE detector.
Nyquist's third criterion for distortionless trasmission is that the area under the system re... more Nyquist's third criterion for distortionless trasmission is that the area under the system response during a unit interval should be propotional to the signal value. It is shown here that for a system characteristic F(ω) to satisfy this criterion, F(w) multiplied by [(sin ωT/2)/(ωT/2)] should satisfy Nyquist's first criterion.
Due to the unique characteristics of sensor devices, finding the energy-efficient modulation with... more Due to the unique characteristics of sensor devices, finding the energy-efficient modulation with a lowcomplexity implementation (refereed to as green modulation) poses significant challenges in the physical layer design of Wireless Sensor Networks (WSNs). Toward this goal, we present an in-depth analysis on the energy efficiency of various modulation schemes using realistic models in the IEEE 802.15.4 standard to find the optimum distance-based scheme in a WSN over Rayleigh and Rician fading channels with path-loss. We describe a proactive system model according to a flexible duty-cycling mechanism utilized in practical sensor apparatus. The present analysis includes the effect of the channel bandwidth and the active mode duration on the energy consumption of popular modulation designs. Path-loss exponent and DC-DC converter efficiency are also taken into consideration. In considering the energy efficiency and complexity, it is demonstrated that among various sinusoidal carrier-based modulations, the optimized Non-Coherent M-ary Frequency Shift Keying (NC-MFSK) is the most energy-efficient scheme in sparse WSNs for each value of the path-loss exponent, where the optimization is performed over the modulation parameters. In addition, we show that the On-Off Keying (OOK) displays a significant energy saving as compared to the optimized NC-MFSK in dense WSNs with small values of path-loss exponent.
IEEE Transactions on Wireless Communications, 2005
The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with... more The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with postdetection equal gain combining (EGC) over generalized fading channels is of great theoretical interest and practical importance. In this paper, by using a decision variable-based moment generating function approach, exact error probability results for DAPSK over generalized Rician and Nakagami fading channels are derived, taking into account the effects of all the system and fading channel parameters. Several maximum likelihood (ML)-based detectors that do not require channel state information (CSI) are proposed for generalized Rician fading channels, and an exact bit error probability (BEP) union bound for the ML detection is derived. Assuming CSI, a performance upper bound for DAPSK with EGC is also presented. Simulation and numerical results show when both detectors have no CSI, the conventional DAPSK detector may perform closely to (though worse than) the ML detector. However, the EGC receiver with CSI performs substantially better than the ML detector without CSI, and very closely to the coherent APSK detector.
IEEE Transactions on Wireless Communications, 2007
ABSTRACT Multiple-input multiple-output (MIMO) system using orthogonal frequency division multipl... more ABSTRACT Multiple-input multiple-output (MIMO) system using orthogonal frequency division multiplexing (OFDM) technique has become a promising method for reliable high data-rate wireless transmission system in which the channel is dispersive in both time and frequency domains. Due to multiple cochannel interferences in a MIMO system, the accuracy of channel estimation is a vital factor for proper receiver design in order to realize the full potential performance of the MIMO-OFDM system. A robust and improved channel estimation algorithm is proposed in this paper for MIMO-OFDM systems based on the least squares (LS) algorithm. The proposed algorithm, called improved LS (ILS), employs the noise correlation in order to reduce the variance of the LS estimation error by estimating and suppressing the noise in signal subspace. The performance of the ILS channel estimation algorithm is robust to the number of antennas in transmit and receive sides. The new algorithm attains a significant improvement in performance in comparison with that of the regular LS estimator. Also, with respect to mean square error criterion and without using channel statistics, the ILS algorithm achieves a performance very close to that of the minimum mean square error (MMSE) estimator in terms of the parameters used in practical MIMO-OFDM systems. A modification of the ILS algorithm, called modified ILS (MILS), is proposed based on using the second order statistical parameters of channel. Analytically, it is shown that the MILS estimator achieves the exact performance of the MMSE estimator. Due to no specific data sequences being required to perform the estimation, in addition to the training mode, the proposed channel estimation algorithms can also be extended and used in the tracking mode with decision-aided method.
IEEE Transactions on Wireless Communications, 2010
Abstract In this letter, a design metric of the interleaver is derived from the union bound of th... more Abstract In this letter, a design metric of the interleaver is derived from the union bound of the bit error rate (BER) of linearly precoded orthogonal frequency division multiplexing (OFDM) systems, assuming that the power-delay profile of the channel is known at the transmitter. A new cyclic shift interleaving scheme is proposed to improve the BER performance of OFDM systems. The proposed interleaving scheme is parameterized, and it incorporates existing interleaving schemes. The simulation results indicate that the proposed interleavers ...
Abstract This paper develops a family of irregular convolutional codes for bit-interleaved coded ... more Abstract This paper develops a family of irregular convolutional codes for bit-interleaved coded modulation (BICM) systems under iterative detection and decoding. Irregular convolutional codes are constructed through irregular puncturing over multiple mother codes of different memory. Strategies based on fixed-and variable-size trellises are proposed to connect different memory mother codes. The use of irregular puncturing and code memory yields improved coding efficiency with the aid of extrinsic information ...
This paper presents an in-depth analysis on the energy efficiency of Luby Transform (LT) codes wi... more This paper presents an in-depth analysis on the energy efficiency of Luby Transform (LT) codes with Frequency Shift Keying (FSK) modulation in a Wireless Sensor Network (WSN) over Rayleigh fading channels with path-loss. We describe a proactive system model according to a flexible duty-cycling mechanism utilized in practical sensor apparatus. The present analysis is based on realistic parameters including the effect of channel bandwidth used in the IEEE 802.15.4 standard, active mode duration and computation energy. A comprehensive analysis, supported by some simulation studies on the probability mass function of the LT code rate and coding gain, shows that among uncoded FSK and various classical channel coding schemes, the optimized LT coded FSK is the most energyefficient scheme for distance d greater than the predetermined threshold level dT , where the optimization is performed over coding and modulation parameters. In addition, although the optimized uncoded FSK outperforms coded schemes for d < dT , the energy gap between LT coded and uncoded FSK is negligible for d < dT compared to the other coded schemes. These results come from the flexibility of the LT code to adjust its rate to suit instantaneous channel conditions, and suggest that LT codes are beneficial in practical low-power WSNs with dynamic position sensor nodes.
Abstract We consider a scenario where n collaborating cognitive radios (CRs) try to jointly detec... more Abstract We consider a scenario where n collaborating cognitive radios (CRs) try to jointly detect spectrum opportunities in a wide-band spectrum within a predefined spectrum sensing interval T S. We assume that each CR is equipped with a tunable bandpass filter (BPF) and is able to sense one frequency band (channel) at a time. The sensing interval consists of L sensing slots of length T. During each sensing slot, each of the collaborating CRs is assigned to sense one of the channels and report its observation to the other CRs. ...
Tables are presented of good ternary and quaternary codes and they are used in the construction o... more Tables are presented of good ternary and quaternary codes and they are used in the construction of dense sphere packings. Results include 1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50, 2) a class of optimal [ n , 21 codes over GF(q), 3) the (U + U + w I2u + U I U) construction, a new ternary code construction technique that can be used to construct the ternary Reed-Muller codes (and others), and 4) tables of linear ternary and quaternary codes obtained by modifying and combining various codes discovered here and in the literature. Using these codes and a sphere-packing construction, packings are generated in even dimensions up to 100. In dimensions 36 and 60, new record densities appear to have been achieved.
A partial ordering on general finite-state Markov channels is given, which orders the channels in... more A partial ordering on general finite-state Markov channels is given, which orders the channels in terms of probability of symbol error under iterative estimation decoding of a low-density parity-check (LDPC) code. This result is intended to mitigate the complexity of characterizing the performance of general finite-state Markov channels, which is difficult due to the large parameter space of this class of channel. An analysis tool, originally developed for the Gilbert-Elliott channel, is extended and generalized to general finite-state Markov channels. In doing so, an operator is introduced for combining finite-state Markov channels to create channels with larger state alphabets, which are then subject to the partial ordering. As a result, the probability of symbol error performance of finite-state Markov channels with different numbers of states and wide ranges of parameters can be directly compared. Several examples illustrating the use of the techniques are provided, focusing on binary finite-state Markov channels and Gaussian finite-state Markov channels. Furthermore, this result is used to order Gilbert-Elliott channels with different marginal state probabilities, which was left as an open problem by previous work. Index Terms-Estimation-decoding, iterative decoding, lowdensity parity-check (LDPC) codes, Markov channels, partial ordering. I. INTRODUCTION F INITE-STATE Markov channels are binary-input channels, each with a hidden channel state sequence that is generated by a finite-state Markov chain, where the state of the Markov chain determines the instantaneous behavior of the channel. (Throughout this paper, we will take the finite-state nature of the channel to be implicit, and simply refer to Markov channels.) These channels have many applications, such as approximating wireless channels with slow fading, or modeling other correlated noise effects. Capacity and coding for these channels was discussed in [1]. A low-density parity-check (LDPC) code is a type of block code with a very sparse parity-check matrix [2]. Using the sum-product algorithm (SPA) [3] for decoding, it is well
We consider a Code Division Multiple Access (CDMA) cellular network and propose sub-optimal multi... more We consider a Code Division Multiple Access (CDMA) cellular network and propose sub-optimal multiuser detectors which exploit a type of diversity inherent in the system and are based on the processing of signals received at multiple base stations. We investigate the performance of conventional matched-lter, linear, and decisionbased detection schemes, using this diversity scheme, for both synchronous and asynchronous systems. The detection of user signals is based on tracking the signals at several base stations. The optimal detector would operate on all the signals received at all the base stations but would have a high degree of complexity. We discuss the case where the detection of a given signal is based on received signals at a small subset of base stations. We show that with judicious selection of this smaller set of base stations, good performance can be obtained without much increase in complexity.
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