Prerequisites & Notation

Before You Begin

The interference channel is perhaps the most challenging multiuser channel model. This chapter requires a solid understanding of the MAC (Chapter 14) and BC (Chapters 15-16) capacity results, as we will contrast the IC with both. The reader should also be comfortable with the random coding and typicality arguments from Part III.

MAC capacity region and successive cancellation(Review ch14)
Self-check: Can you state the two-user MAC capacity region and explain how SIC achieves the corner points?
Broadcast channel coding: superposition and DPC(Review ch16)
Self-check: Can you explain how DPC achieves the MIMO BC capacity and why the BC converse uses channel enhancement?
Channel coding theorem: achievability and converse(Review ch09)
Self-check: Can you state Fano's inequality and use it in a converse proof?
Joint typicality and the packing/covering lemmas(Review ch03)
Self-check: Can you state the packing lemma and explain the exponential decay of the error probability?
Linear algebra: subspaces, projections, rank
Self-check: Given two subspaces of $\mathbb{R}^n$ , can you determine their intersection and the dimension of their sum?

Notation for This Chapter

Key symbols for the interference channel. We use subscripts 1, 2 for the two transmitter-receiver pairs, and cross-channel gains $a, b$ for the interference links.

Symbol	Meaning	Introduced
$a, b$	Cross-channel gains: $a$ = interference from Tx 2 to Rx 1, $b$ = interference from Tx 1 to Rx 2	s01
$R_{1}, R_{2}$	Communication rates for pairs 1 and 2	s01
$R_{0k}, R_{pk}$	Common and private message rates for user $k$ (Han-Kobayashi)	s03
$\text{DoF}$	Degrees of freedom: $\lim_{\text{SNR} \to \infty} C(\text{SNR}) / \log(\text{SNR})$	s04
$P_1, P_2$	Transmit power constraints for users 1 and 2	s01
$\sigma^2$	Noise variance (assumed equal at both receivers)	s01
$\text{INR}$	Interference-to-noise ratio: $a^2 P_2 / \sigma^2$ at Rx 1	s01
$\mathbf{V}_k$	Precoding matrix for user $k$ (interference alignment)	s04

← Ch 16 The Two-User Interference Channel