Capacity Region of the Reciprocal Deterministic 3-Way Channel via Delta-Y Transformation


H. Maier, A. Chaaban, R. Mathar, A. Sezgin,


        A linear shift deterministic 3-way channel with reciprocal channel gains is considered in this work. The 3-way channel is an extension of the 2-way channel introduced by Shannon. Here, a number of six messages is exchanged, one message from each user to the two other users. Each user operates in a full-duplex mode. We derive the capacity region of this 3-way channel w.r.t. the linear shift deterministic channel model. To this end, first, an outer bound is derived using cut-set and genie-aided upper bounds. Then, it is noted that the outer bound bears a resemblance to the capacity region of a related linear shift deterministic Y - channel. Utilizing a ?-Y transformation, the optimal scheme for the related Y - channel is modified in a way that achieves the outer bound of the 3-way channel. Mainly, the capacity achieving communication schemes are based on multi-way relaying by signal alignment, interference neutralization and backward decoding. We also consider a scheme which is based on interference alignment only. It turns out, that for the symmetric linear deterministic 3- way channel, this scheme is optimal. Thus, backward decoding and the resulting delays are avoided.

BibTEX Reference Entry 

	author = {Henning Maier and Anas Chaaban and Rudolf Mathar and Aydin Sezgin},
	title = "Capacity Region of the Reciprocal Deterministic 3-Way Channel via Delta-Y Transformation",
	pages = "167-174",
	booktitle = "52nd Annual Allerton Conference on Communication, Control and Computing",
	address = {Monticello, Illinois, USA},
	month = Oct,
	year = 2014,


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