Abstract
We provide inner and outer bounds on the capacity region for the Gaussian bi-directional relaying over inter-symbol interference channels. The outer bound is obtained by the conventional cut-set argument. For the inner bound, we propose a compute-and-forward coding scheme based on lattice partition chains and study its achievable rate. The coding scheme is a time-domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords. The proposed compute-and-forward coding scheme substantially outperforms decode-and-forward schemes. While it is well known that for the point-to-point communication case, both independent coding along sub-channels and time-domain coding can approach the capacity limit, as a byproduct of the proposed scheme, we show that for the bi-directional relay case, independent coding along sub-channels is not optimal in general and joint coding across sub-channels can improve the capacity for some channel realizations.
Original language | English |
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Pages (from-to) | 1011-1019 |
Number of pages | 9 |
Journal | IEEE Transactions on Communications |
Volume | 61 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2013 |
Keywords
- Bi-directional relay channels
- two way relay channels
- compute and forward
- physical layer network coding
- and inter-symbol interference
- DECISION-FEEDBACK EQUALIZERS
- INTERSYMBOL INTERFERENCE
- CHANNEL
- CAPACITY
- NETWORK
- CODES