### Abstract

A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large.

Original language | English (US) |
---|---|

Article number | 6340387 |

Pages (from-to) | 4503-4513 |

Number of pages | 11 |

Journal | IEEE Transactions on Wireless Communications |

Volume | 11 |

Issue number | 12 |

DOIs | |

State | Published - 2012 |

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### Keywords

- frequency-selective channel
- joint decoding
- list decoding
- MMSE detection
- performance analysis
- physical-layer network coding
- Two-way relay channels
- union bounds

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Science Applications
- Applied Mathematics

### Cite this

*IEEE Transactions on Wireless Communications*,

*11*(12), 4503-4513. [6340387]. https://doi.org/10.1109/TWC.2012.101112.120190

**Decoding strategies at the relay with physical-layer network coding.** / Bhat, Uttam; Duman, Tolga M.

Research output: Contribution to journal › Article

*IEEE Transactions on Wireless Communications*, vol. 11, no. 12, 6340387, pp. 4503-4513. https://doi.org/10.1109/TWC.2012.101112.120190

}

TY - JOUR

T1 - Decoding strategies at the relay with physical-layer network coding

AU - Bhat, Uttam

AU - Duman, Tolga M.

PY - 2012

Y1 - 2012

N2 - A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large.

AB - A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large.

KW - frequency-selective channel

KW - joint decoding

KW - list decoding

KW - MMSE detection

KW - performance analysis

KW - physical-layer network coding

KW - Two-way relay channels

KW - union bounds

UR - http://www.scopus.com/inward/record.url?scp=84871810490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871810490&partnerID=8YFLogxK

U2 - 10.1109/TWC.2012.101112.120190

DO - 10.1109/TWC.2012.101112.120190

M3 - Article

AN - SCOPUS:84871810490

VL - 11

SP - 4503

EP - 4513

JO - IEEE Transactions on Wireless Communications

JF - IEEE Transactions on Wireless Communications

SN - 1536-1276

IS - 12

M1 - 6340387

ER -