Approximation of the Error Probability in a Regenerative Repeater with Quantized Feedback

Aaron, M. R.; Simon, M

doi:10.1002/j.1538-7305.1966.tb02440.x

Cited by 16 publications

(5 citation statements)

References 2 publications

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“…Section V modifies the results of Section III by including the case of imperfect match of the G (s) and H (8) characteristics.…”

mentioning

confidence: 96%

“…(iii) G (8) and H (8) are exact complements of each other so that perfect feedback tail cancellation is achieved.…”

mentioning

confidence: 98%

“…(ii) The low-frequency behavior of the channel as represented by G (8) is dominated by a single pole.…”

mentioning

confidence: 99%

“…(iv) The time dispersion of the transmitted pulses caused by the medium, C (8), with or without equalization E (8) is strictly limited to two pulse intervals.…”

mentioning

confidence: 99%

“…An application of the results is given for a particular high-frequency behavior of the system. The response of the high-frequency portion of the channel, C (8) E (8), to a transmitted rectangular pulse is assumed triangular in shape and time-limited to two pulse intervals.…”

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confidence: 99%

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Extensions to the Analysis of Regenerative Repeaters with Quantized Feedback

Simon¹

1967

Bell System Technical Journal

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The functional iterative approach given by Zador for calculating the average bit error probability in a regenerative repeater with quantized feedback is extended to the vector case. For a channel with a rational fraction transfer function, the vector extension permits us at least formally to deal with the following practical conditions: (~) The pulse transmission plan is described by an m-ary alphabet with independent digits.(ii) Perfect and imperfect low-frequency tail cancellation cases are considered.(iii) High-frequency signal shaping and its interaction with the predominantly low-frequency tail are taken into account.Expressions for error probability on the kth digit are derived in terms of the kth vector iterate of a known function. The restriction to independent noise samples is also removed. The resulting expression for kth bit error probability is then derived from an operational iteration procedure which acts on the k + 1 dimensional joint distribution of the noise samples.

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“…Section V modifies the results of Section III by including the case of imperfect match of the G (s) and H (8) characteristics.…”

mentioning

confidence: 96%

“…(iii) G (8) and H (8) are exact complements of each other so that perfect feedback tail cancellation is achieved.…”

mentioning

confidence: 98%

“…(ii) The low-frequency behavior of the channel as represented by G (8) is dominated by a single pole.…”

mentioning

confidence: 99%

“…(iv) The time dispersion of the transmitted pulses caused by the medium, C (8), with or without equalization E (8) is strictly limited to two pulse intervals.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Extensions to the Analysis of Regenerative Repeaters with Quantized Feedback

Simon¹

1967

Bell System Technical Journal

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Analysis of error propagation and design of filter cutoff frequency in a quantized feedback dc‐restoration system

Yamaguchi

1988

Electron. Comm. Jpn. Pt. I

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In the regenerative repeater in digital transmission, the low‐frequency component of the transmitted pulse is cut off by the coupling circuits at the input and the output. However, by applying the quantized feedback dc‐restoration circuit in the repeater the digital regenerative transmission with low dc‐balance transmission code can be achieved. In the quantized feedback system, the component lost in the low‐frequency cutoff characteristics of the transmission system is restored by feeding back the low‐frequency component of the pulse regenerated in the repeater to the decision circuit input. Because of this mechanism, however, an error propagation occurs where an error component is fed back to produce a distortion and to enlarge the error, when a decision error is produced in the repeater. This paper derives the state‐transition diagram which approximates the error propagation. By the analysis of the state‐transition diagram, the relation between the filter cutoff frequency and the error propagation characteristics is determined. Furthermore, it is shown by a simulation experiment that the result of the analysis is a good approximation to the error propagation. Based on these results, a design method is presented for the cutoff frequencies of the forward and the feedback low‐pass filters in the quantized feedback system.

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Adaptive Redundancy Removal in Data Transmission

Lucky¹

1968

Bell System Technical Journal

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Approximation of the Error Probability in a Regenerative Repeater with Quantized Feedback

Cited by 16 publications

References 2 publications

Extensions to the Analysis of Regenerative Repeaters with Quantized Feedback

Extensions to the Analysis of Regenerative Repeaters with Quantized Feedback

Analysis of error propagation and design of filter cutoff frequency in a quantized feedback dc‐restoration system

Adaptive Redundancy Removal in Data Transmission

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