Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02010.X
D. Gloge, E. Marcatili
The index distribution in the cross section of a multimode fiber has an important influence on the modal group velocities and, hence, on the fiber impulse response. In this paper we derive a method for the evaluation of arbitrary circular symmetric index profiles. In particular, we compute the impulse response of a fiber with a ring-shaped parabolic index profile which exhibits useful equalizing properties. The pulse spread is found to be nearly one order of magnitude smaller than that of a fiber with an equal, but abrupt, index decline from core to cladding.
{"title":"Impulse response of fibers with ring-shaped parabolic index distribution","authors":"D. Gloge, E. Marcatili","doi":"10.1002/J.1538-7305.1973.TB02010.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02010.X","url":null,"abstract":"The index distribution in the cross section of a multimode fiber has an important influence on the modal group velocities and, hence, on the fiber impulse response. In this paper we derive a method for the evaluation of arbitrary circular symmetric index profiles. In particular, we compute the impulse response of a fiber with a ring-shaped parabolic index profile which exhibits useful equalizing properties. The pulse spread is found to be nearly one order of magnitude smaller than that of a fiber with an equal, but abrupt, index decline from core to cladding.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"66 1","pages":"1161-1168"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78196872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02008.X
N. Jayant
We discuss a quantizer which, for every new input sample, adapts its step-size by a factor depending only on the knowledge of which quantizer slot was occupied by the previous signal sample.1 Specifically, if the outputs of a uniform B-bit quantizer (B > 1) are of the form the step-size Δ r , is given by the previous step-size multiplied by a time-invariant function of the code-word magnitude: The adaptations are motivated by the assumption that the input signal variance is unknown, so that the quantizer is started off, in general, with a suboptimal step-size Δ START . Multiplier functions that maximize the signal-to-quantization-error ratio (SNR) depend, in general, on Δ START and the input sequence length N. For example, if the signal is stationary and N → ∞ best multipliers, irrespective of Δ START , have values arbitrarily close to unity. On the other hand, small values of N and suboptimal values of Δ START necessitate M values further away from unity. By including an adequate range of values for N and Δ START in a generalized SNR definition, we show how one can determine stable multiplier functions M OPT that are optimal for a given signal. In computer simulations of 2- and 3-bit quantizers with first-order Gauss-Markovian inputs, we note that, except when the magnitude of the correlation C between adjacent samples is very high, M OPT has the property of calling for fast increases and slow decreases of step-size. We derive optimum multipliers theoretically for two simple cases:
{"title":"Adaptive quantization with a one-word memory","authors":"N. Jayant","doi":"10.1002/J.1538-7305.1973.TB02008.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02008.X","url":null,"abstract":"We discuss a quantizer which, for every new input sample, adapts its step-size by a factor depending only on the knowledge of which quantizer slot was occupied by the previous signal sample.1 Specifically, if the outputs of a uniform B-bit quantizer (B > 1) are of the form the step-size Δ r , is given by the previous step-size multiplied by a time-invariant function of the code-word magnitude: The adaptations are motivated by the assumption that the input signal variance is unknown, so that the quantizer is started off, in general, with a suboptimal step-size Δ START . Multiplier functions that maximize the signal-to-quantization-error ratio (SNR) depend, in general, on Δ START and the input sequence length N. For example, if the signal is stationary and N → ∞ best multipliers, irrespective of Δ START , have values arbitrarily close to unity. On the other hand, small values of N and suboptimal values of Δ START necessitate M values further away from unity. By including an adequate range of values for N and Δ START in a generalized SNR definition, we show how one can determine stable multiplier functions M OPT that are optimal for a given signal. In computer simulations of 2- and 3-bit quantizers with first-order Gauss-Markovian inputs, we note that, except when the magnitude of the correlation C between adjacent samples is very high, M OPT has the property of calling for fast increases and slow decreases of step-size. We derive optimum multipliers theoretically for two simple cases:","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"44 1","pages":"1119-1144"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76991646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02012.X
S. Personick
If a sequence of digitally on-off modulated optical pulses is injected into a dielectric waveguide, these pulses may begin to overlap after a sufficient distance of propagation because of material dispersion and/or group delay spreading. In general, the pulses will not add linearly in power, which can complicate the problem of equalization of the square-law (power) detected overlapping output pulses at baseband. This paper illustrates important situations in which the guide may be treated as “pseudo-linear” in power, meaning that the detected guide output pulses appear to add linearly.
{"title":"Baseband linearity and equalization in fiber optic digital communication systems","authors":"S. Personick","doi":"10.1002/J.1538-7305.1973.TB02012.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02012.X","url":null,"abstract":"If a sequence of digitally on-off modulated optical pulses is injected into a dielectric waveguide, these pulses may begin to overlap after a sufficient distance of propagation because of material dispersion and/or group delay spreading. In general, the pulses will not add linearly in power, which can complicate the problem of equalization of the square-law (power) detected overlapping output pulses at baseband. This paper illustrates important situations in which the guide may be treated as “pseudo-linear” in power, meaning that the detected guide output pulses appear to add linearly.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"100 1","pages":"1175-1194"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74824206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02004.X
D. Slepian, Jack Keil Wolfd
A communication system is studied in which two users communicate with one receiver over a common discrete memoryless channel. The information to be transmitted by the users may be correlated. Their information rates are described by a point in a suitably defined three-dimensional rate space. A point in this rate space is called admissible if there exist coders and decoders for the channel that permit the users to transmit information over it at the corresponding rates with arbitrarily small error probability. The closure of the set of all admissible rate points is called the capacity region, and is the natural generalization of channel capacity to this situation. In this paper we show that e, which depends only on the channel, is convex and we give formulas to determine it exactly. Several simple channels are treated in detail and their capacity regions given explicitly.
{"title":"A coding theorem for multiple access channels with correlated sources","authors":"D. Slepian, Jack Keil Wolfd","doi":"10.1002/J.1538-7305.1973.TB02004.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02004.X","url":null,"abstract":"A communication system is studied in which two users communicate with one receiver over a common discrete memoryless channel. The information to be transmitted by the users may be correlated. Their information rates are described by a point in a suitably defined three-dimensional rate space. A point in this rate space is called admissible if there exist coders and decoders for the channel that permit the users to transmit information over it at the corresponding rates with arbitrarily small error probability. The closure of the set of all admissible rate points is called the capacity region, and is the natural generalization of channel capacity to this situation. In this paper we show that e, which depends only on the channel, is convex and we give formulas to determine it exactly. Several simple channels are treated in detail and their capacity regions given explicitly.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"31 1","pages":"1037-1076"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86766701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02007.X
P. Cummiskey, N. Jayant, J. Flanagan
We describe an adaptive differential PCM (ADPCM) coder which makes instantaneous exponential changes of quantizer step-size. The coder includes a simple first-order predictor and a time-invariant, minimally complex adaptation strategy. Step-size multipliers depend only on the most recent quantizer output, and input signals of unknown variance can be accommodated. We derive appropriate multiplier values from computer simulations with speech signals and with Gauss-Markov inputs. We compare performance of the ADPCM coder with conventional log-PCM, using both objective and subjective criteria. Finally, we describe an economical integrated hardware implementation of the ADPCM coder. We believe that at bit rates of 24 to 32 kb/s, ADPCM provides a robust and efficient technique for speech communication and for digital storage of speech.
{"title":"Adaptive quantization in differential PCM coding of speech","authors":"P. Cummiskey, N. Jayant, J. Flanagan","doi":"10.1002/J.1538-7305.1973.TB02007.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02007.X","url":null,"abstract":"We describe an adaptive differential PCM (ADPCM) coder which makes instantaneous exponential changes of quantizer step-size. The coder includes a simple first-order predictor and a time-invariant, minimally complex adaptation strategy. Step-size multipliers depend only on the most recent quantizer output, and input signals of unknown variance can be accommodated. We derive appropriate multiplier values from computer simulations with speech signals and with Gauss-Markov inputs. We compare performance of the ADPCM coder with conventional log-PCM, using both objective and subjective criteria. Finally, we describe an economical integrated hardware implementation of the ADPCM coder. We believe that at bit rates of 24 to 32 kb/s, ADPCM provides a robust and efficient technique for speech communication and for digital storage of speech.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"6 1","pages":"1105-1118"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80865355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02013.X
R. Franks, R. Rishel
A telephone network with switching and trunk congestion is considered. An optimization problem expressed in terms of mean numbers of calls and mean rates of flow of calls in various categories of service throughout the network is formulated. The maximum mean number of talking calls given by this optimization problem is an upper bound on the mean number of talking calls which could be carried by the network using theoretically optimum network management. Examples are given suggesting that the upper bound is close to values which actually can be attained. The optimum of the problem is achieved by controls which (i) restrict the number of calls coming into the network from the end offices and (ii) route appropriate fractions of the remaining calls over the various possible routes.
{"title":"Optimum network call-carrying capacity","authors":"R. Franks, R. Rishel","doi":"10.1002/J.1538-7305.1973.TB02013.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02013.X","url":null,"abstract":"A telephone network with switching and trunk congestion is considered. An optimization problem expressed in terms of mean numbers of calls and mean rates of flow of calls in various categories of service throughout the network is formulated. The maximum mean number of talking calls given by this optimization problem is an upper bound on the mean number of talking calls which could be carried by the network using theoretically optimum network management. Examples are given suggesting that the upper bound is close to values which actually can be attained. The optimum of the problem is achieved by controls which (i) restrict the number of calls coming into the network from the end offices and (ii) route appropriate fractions of the remaining calls over the various possible routes.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"71 1","pages":"1195-1214"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73840226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02011.X
D. Marcuse
To the paraxial approximation there is no difference in the group delay of the modes of a parabolic index fiber. However, the wave optics treatment of the infinitely extended parabolic index medium predicts a slight difference in the group delay of the various modes. This result is used in this paper to predict the shape and width of the impulse response function of a parabolic index fiber with finite radius.
{"title":"The impulse response of an optical fiber with parabolic index profile","authors":"D. Marcuse","doi":"10.1002/J.1538-7305.1973.TB02011.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02011.X","url":null,"abstract":"To the paraxial approximation there is no difference in the group delay of the modes of a parabolic index fiber. However, the wave optics treatment of the infinitely extended parabolic index medium predicts a slight difference in the group delay of the various modes. This result is used in this paper to predict the shape and width of the impulse response function of a parabolic index fiber with finite radius.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"1 1","pages":"1169-1174"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75703732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02014.X
H. Heffes
This paper treats the problem of analyzing a first-come first-served queuing system, in equilibrium, when subjected to a peaked input (e.g., traffic overflowing a trunk group with Poisson input). The basic GI/M/N (renewal input to N exponential servers) queuing result is used, together with each of two models for representing peaked traffic, the Equivalent Random (E-R) model and the Interrupted Poisson Process (IPP) model. The equilibrium virtual delay distribution is derived and compared with the equilibrium distribution of delays seen by arriving calls. Numerical examples are presented, along with comparisons of results using both the above models. The results show that delays can be quite sensitive to peakedness.
{"title":"Analysis of first-come first-served queuing systems with peaked inputs","authors":"H. Heffes","doi":"10.1002/J.1538-7305.1973.TB02014.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02014.X","url":null,"abstract":"This paper treats the problem of analyzing a first-come first-served queuing system, in equilibrium, when subjected to a peaked input (e.g., traffic overflowing a trunk group with Poisson input). The basic GI/M/N (renewal input to N exponential servers) queuing result is used, together with each of two models for representing peaked traffic, the Equivalent Random (E-R) model and the Interrupted Poisson Process (IPP) model. The equilibrium virtual delay distribution is derived and compared with the equilibrium distribution of delays seen by arriving calls. Numerical examples are presented, along with comparisons of results using both the above models. The results show that delays can be quite sensitive to peakedness.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"18 1","pages":"1215-1228"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74613433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02005.X
F. Brophy, G. Foschini, R. Gitlin
We give a solution to the problem of designing a fixed compromise equalizer for use in transmission systems involving an ensemble of random channels. The signal and noise spectra, along with the second-order statistics of the channel ensemble, are used to find the equalizer characteristic that minimizes the mean-square distortion between the equalizer output and a scaled version of the transmitter output. The key departure from previous work is that the criterion better captures practical performance invariance; specifically, the cost function incorporates the insensitivity of a well-designed demodulator to any amplitude scaling or time delay introduced by a particular channel. After demonstrating that the optimum equalizer shape is related to the principal eigenfunction of a normalized channel correlation function, we consider several special cases that give further insight into the properties of the solution. We find that the equalizer amplitude is attenuated over those frequencies where the signal-to-noise or signal-to-channel-variance ratios are small. The analysis confirms the standard engineering practice of inverting the average channel in the absence of noise and when the variance of the channel characteristics is small.
{"title":"A compromise equalizer design incorporating performance invariance","authors":"F. Brophy, G. Foschini, R. Gitlin","doi":"10.1002/J.1538-7305.1973.TB02005.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02005.X","url":null,"abstract":"We give a solution to the problem of designing a fixed compromise equalizer for use in transmission systems involving an ensemble of random channels. The signal and noise spectra, along with the second-order statistics of the channel ensemble, are used to find the equalizer characteristic that minimizes the mean-square distortion between the equalizer output and a scaled version of the transmitter output. The key departure from previous work is that the criterion better captures practical performance invariance; specifically, the cost function incorporates the insensitivity of a well-designed demodulator to any amplitude scaling or time delay introduced by a particular channel. After demonstrating that the optimum equalizer shape is related to the principal eigenfunction of a normalized channel correlation function, we consider several special cases that give further insight into the properties of the solution. We find that the equalizer amplitude is attenuated over those frequencies where the signal-to-noise or signal-to-channel-variance ratios are small. The analysis confirms the standard engineering practice of inverting the average channel in the absence of noise and when the variance of the channel characteristics is small.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"1 1","pages":"1077-1095"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87664602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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