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Transmission of a bit over a discrete Poisson channel with memory

Ahmadypour, N ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1109/ITW46852.2021.9457575
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2021
  4. Abstract:
  5. A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we find the best codebook design by minimizing the error probability of the decoder over all codebooks. For the case of having only a total-power constraint, the optimal code structure is obtained provided that the blocklength is greater than the memory length of the channel. For the case of having only a peak-power constraint, the optimal code is derived for arbitrary memory and blocklength in the high-power regime. For the case of having both the peak-power and total-power constraints, the optimal code is derived for memoryless Poisson channels when both the total-power and the peak-power bounds are large. ©2021 IEEE
  6. Keywords:
  7. Additive noise ; Decoding ; Maximum likelihood ; Optimal systems ; Structural optimization ; Transmissions ; Channel inputs ; Codebook design ; Distributed random variables ; Error probabilities ; Linear combinations ; Maximum likelihood decoders ; Peak-power constraints ; Poisson channel ; Channel coding
  8. Source: 2020 IEEE Information Theory Workshop, ITW 2020, 11 April 2021 through 15 April 2021 ; 2021 ; 9781728159621 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/9424631