### Abstract

This paper characterizes an achievable channel coding rate for a noiseless binary communication channel with an energy harvesting (EH) transmitter at a given blocklength n and error probability ε. As energy arrives randomly at the transmitter, codewords must obey the cumulative stochastic energy constraints. The coupling of the energy constraints on the symbols in a codeword makes the analysis fundamentally different from that of discrete memoryless channels. We first adopt a random coding scheme to construct the codebook with statistical information of the EH process. We then analyze the statistics of the corresponding output sequence. Specifically, we prove that the average number of mismatches between the input codeword and the output sequence scales as O(√n). Based on such characterization, we then propose a decoding scheme, and analyze the corresponding probability of decoding error. Finally, we explicitly characterize the maximum size of the length-n codebook generated by the random coding scheme in order to achieve the average probability of error ε. This leads to a lower bound on the maximum achievable channel coding rate for the EH communication channel. We show that the gap between the lower bound and the corresponding channel capacity under an equivalent average power constraint scales in O(llog n/√n), where l is a constant depending on the error probability ?, and the statistics of the energy harvesting process.

Original language | English (US) |
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Title of host publication | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 811-815 |

Number of pages | 5 |

ISBN (Print) | 9781479951864 |

DOIs | |

State | Published - 2014 |

Event | 2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States Duration: Jun 29 2014 → Jul 4 2014 |

### Other

Other | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |
---|---|

Country | United States |

City | Honolulu, HI |

Period | 6/29/14 → 7/4/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Cite this

*2014 IEEE International Symposium on Information Theory, ISIT 2014*(pp. 811-815). [6874945] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6874945

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*2014 IEEE International Symposium on Information Theory, ISIT 2014.*, 6874945, Institute of Electrical and Electronics Engineers Inc., pp. 811-815, 2014 IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, United States, 6/29/14. https://doi.org/10.1109/ISIT.2014.6874945

**Achievable rate for energy harvesting channel with finite blocklength.** / Yang, Jing.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Achievable rate for energy harvesting channel with finite blocklength

AU - Yang, Jing

PY - 2014

Y1 - 2014

N2 - This paper characterizes an achievable channel coding rate for a noiseless binary communication channel with an energy harvesting (EH) transmitter at a given blocklength n and error probability ε. As energy arrives randomly at the transmitter, codewords must obey the cumulative stochastic energy constraints. The coupling of the energy constraints on the symbols in a codeword makes the analysis fundamentally different from that of discrete memoryless channels. We first adopt a random coding scheme to construct the codebook with statistical information of the EH process. We then analyze the statistics of the corresponding output sequence. Specifically, we prove that the average number of mismatches between the input codeword and the output sequence scales as O(√n). Based on such characterization, we then propose a decoding scheme, and analyze the corresponding probability of decoding error. Finally, we explicitly characterize the maximum size of the length-n codebook generated by the random coding scheme in order to achieve the average probability of error ε. This leads to a lower bound on the maximum achievable channel coding rate for the EH communication channel. We show that the gap between the lower bound and the corresponding channel capacity under an equivalent average power constraint scales in O(llog n/√n), where l is a constant depending on the error probability ?, and the statistics of the energy harvesting process.

AB - This paper characterizes an achievable channel coding rate for a noiseless binary communication channel with an energy harvesting (EH) transmitter at a given blocklength n and error probability ε. As energy arrives randomly at the transmitter, codewords must obey the cumulative stochastic energy constraints. The coupling of the energy constraints on the symbols in a codeword makes the analysis fundamentally different from that of discrete memoryless channels. We first adopt a random coding scheme to construct the codebook with statistical information of the EH process. We then analyze the statistics of the corresponding output sequence. Specifically, we prove that the average number of mismatches between the input codeword and the output sequence scales as O(√n). Based on such characterization, we then propose a decoding scheme, and analyze the corresponding probability of decoding error. Finally, we explicitly characterize the maximum size of the length-n codebook generated by the random coding scheme in order to achieve the average probability of error ε. This leads to a lower bound on the maximum achievable channel coding rate for the EH communication channel. We show that the gap between the lower bound and the corresponding channel capacity under an equivalent average power constraint scales in O(llog n/√n), where l is a constant depending on the error probability ?, and the statistics of the energy harvesting process.

UR - http://www.scopus.com/inward/record.url?scp=84906562416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906562416&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2014.6874945

DO - 10.1109/ISIT.2014.6874945

M3 - Conference contribution

SN - 9781479951864

SP - 811

EP - 815

BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014

PB - Institute of Electrical and Electronics Engineers Inc.

ER -