Abstract
The paper addresses Wireless Physical Layer Network Coding (WPNC) with Hierarchical Decode and Forward (HDF) strategy. We analyze achievable hierarchical rates in one stage hierarchical MAC (H-MAC) channel for higher order component constellations with bit-wise Hierarchical Network Code (HNC) maps. This is motivated by a possible application of state-of-the-art binary (e.g, LDPC) codes over higher order constellations. We show that the bit-mapped binary codes do not have the same achievable rates as direct higher-order codes. On top of this, the individual bits in the HNC map might provide very uneven performance and it strongly depends on the combination of component alphabets. The results are supported by a validation with practical LDPC codes.
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