Variable-Length Sparse Feedback Codes for Point-to-Point, Multiple Access, and Random Access Channels

This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> de...

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Veröffentlicht in:	IEEE transactions on information theory Jg. 70; H. 4; S. 2367 - 2394
Hauptverfasser:	Yavas, Recep Can, Kostina, Victoria, Effros, Michelle
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.04.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	channel dispersion Channels Codes Convergence Decoding Encoding Error probability Feedback feedback codes moderate deviations Multiple access Random access Receivers second-order analysis sequential hypothesis testing sparse feedback Transmitters Variable-length coding
ISSN:	0018-9448, 1557-9654
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Abstract	This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> decoding times <inline-formula> <tex-math notation="LaTeX">n_{1}, n_{2}, {\dots }, n_{L} </tex-math></inline-formula> for the point-to-point and multiple access channels and <inline-formula> <tex-math notation="LaTeX">KL + 1 </tex-math></inline-formula> decoding times for the random access channel with at most <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> active transmitters. In the point-to-point and multiple access channels, the decoder uses the observed channel outputs to decide whether to decode at each of the allowed decoding times <inline-formula> <tex-math notation="LaTeX">n_{1}, {\dots }, n_{L} </tex-math></inline-formula>, at each time telling the encoder whether or not to stop transmitting using a single bit of feedback. In the random access scenario, the decoder estimates the number of active transmitters at time <inline-formula> <tex-math notation="LaTeX">n_{0} </tex-math></inline-formula> and then chooses among decoding times <inline-formula> <tex-math notation="LaTeX">n_{k, 1}, {\dots }, n_{k, L} </tex-math></inline-formula> if it believes that there are <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> active transmitters. In all cases, the choice of allowed decoding times is part of the code design; given fixed value <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>, allowed decoding times are chosen to minimize the expected decoding time for a given codebook size and target average error probability. The number <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> in each scenario is assumed to be constant even when the blocklength is allowed to grow; the resulting code therefore requires only sparse feedback. The central results are asymptotic approximations of achievable rates as a function of the error probability, the expected decoding time, and the number of decoding times. A converse for variable-length stop-feedback codes with uniformly-spaced decoding times is included for the point-to-point channel.
AbstractList	This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> decoding times <inline-formula> <tex-math notation="LaTeX">n_{1}, n_{2}, {\dots }, n_{L} </tex-math></inline-formula> for the point-to-point and multiple access channels and <inline-formula> <tex-math notation="LaTeX">KL + 1 </tex-math></inline-formula> decoding times for the random access channel with at most <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> active transmitters. In the point-to-point and multiple access channels, the decoder uses the observed channel outputs to decide whether to decode at each of the allowed decoding times <inline-formula> <tex-math notation="LaTeX">n_{1}, {\dots }, n_{L} </tex-math></inline-formula>, at each time telling the encoder whether or not to stop transmitting using a single bit of feedback. In the random access scenario, the decoder estimates the number of active transmitters at time <inline-formula> <tex-math notation="LaTeX">n_{0} </tex-math></inline-formula> and then chooses among decoding times <inline-formula> <tex-math notation="LaTeX">n_{k, 1}, {\dots }, n_{k, L} </tex-math></inline-formula> if it believes that there are <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> active transmitters. In all cases, the choice of allowed decoding times is part of the code design; given fixed value <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>, allowed decoding times are chosen to minimize the expected decoding time for a given codebook size and target average error probability. The number <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> in each scenario is assumed to be constant even when the blocklength is allowed to grow; the resulting code therefore requires only sparse feedback. The central results are asymptotic approximations of achievable rates as a function of the error probability, the expected decoding time, and the number of decoding times. A converse for variable-length stop-feedback codes with uniformly-spaced decoding times is included for the point-to-point channel. This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ [Formula Omitted] decoding times [Formula Omitted] for the point-to-point and multiple access channels and [Formula Omitted] decoding times for the random access channel with at most [Formula Omitted] active transmitters. In the point-to-point and multiple access channels, the decoder uses the observed channel outputs to decide whether to decode at each of the allowed decoding times [Formula Omitted], at each time telling the encoder whether or not to stop transmitting using a single bit of feedback. In the random access scenario, the decoder estimates the number of active transmitters at time [Formula Omitted] and then chooses among decoding times [Formula Omitted] if it believes that there are [Formula Omitted] active transmitters. In all cases, the choice of allowed decoding times is part of the code design; given fixed value [Formula Omitted], allowed decoding times are chosen to minimize the expected decoding time for a given codebook size and target average error probability. The number [Formula Omitted] in each scenario is assumed to be constant even when the blocklength is allowed to grow; the resulting code therefore requires only sparse feedback. The central results are asymptotic approximations of achievable rates as a function of the error probability, the expected decoding time, and the number of decoding times. A converse for variable-length stop-feedback codes with uniformly-spaced decoding times is included for the point-to-point channel.
Author	Effros, Michelle Yavas, Recep Can Kostina, Victoria
Author_xml	– sequence: 1 givenname: Recep Can orcidid: 0000-0002-5640-515X surname: Yavas fullname: Yavas, Recep Can email: recep.yavas@cnrsatcreate.sg organization: Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA – sequence: 2 givenname: Victoria orcidid: 0000-0002-2406-7440 surname: Kostina fullname: Kostina, Victoria email: vkostina@caltech.edu organization: Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA – sequence: 3 givenname: Michelle orcidid: 0000-0003-3757-0675 surname: Effros fullname: Effros, Michelle email: effros@caltech.edu organization: Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA
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SubjectTerms	channel dispersion Channels Codes Convergence Decoding Encoding Error probability Feedback feedback codes moderate deviations Multiple access Random access Receivers second-order analysis sequential hypothesis testing sparse feedback Transmitters Variable-length coding
Title	Variable-Length Sparse Feedback Codes for Point-to-Point, Multiple Access, and Random Access Channels
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