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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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- Type of Document: Article
- DOI: 10.1109/TIT.2021.3077872
- Publisher: Institute of Electrical and Electronics Engineers Inc , 2021
- Abstract:
- A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated with 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 of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a closed-form analytical expression. 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. © 1963-2012 IEEE
- Keywords:
- Additive noise ; Codes (symbols) ; Maximum likelihood ; Optimal systems ; Structural optimization ; Transmissions ; Analytical expressions ; Channel inputs ; Distributed random variables ; Error probabilities ; Linear combinations ; Maximum likelihood decoders ; Peak-power constraints ; Poisson channel ; Channel coding
- Source: IEEE Transactions on Information Theory ; Volume 67, Issue 7 , 2021 , Pages 4710-4727 ; 00189448 (ISSN)
- URL: https://ieeexplore.ieee.org/document/9424631