Interference as Noise: Friend or Foe?

Abstract

This paper shows that for the two-user Gaussian interference channel (G-IC) treating interference as noise without time sharing (TINnoTS) achieves the closure of the capacity region to within either a constant gap, or to within a gap of the order O(log(ln(min(S, I))/γ )) up to a set of Lebesgue measure γ ∈ (0, 1], where S is the largest signal to noise ratio on the direct links and I is the largest interference to noise ratio on the cross links. As a consequence, TINnoTS is optimal from a generalized degrees of freedom (gDoF) perspective for all channel gains except for a subset of zero measure. TINnoTS with Gaussian inputs is known to be optimal within 1/2 bit for a subset of the weak interference regime. Rather surprisingly, this paper shows that TINnoTS is gDoF optimal in all parameter regimes, even in the strong and very strong interference regimes where joint decoding of Gaussian inputs is optimal. For approximate optimality of TINnoTS in all parameter regimes, it is critical to use non-Gaussian inputs. This paper thus proposes to use mixed inputs as channel inputs for the G-IC, where a mixed input is the sum of a discrete and a Gaussian random variable. Interestingly, with reference to the Han-Kobayashi achievable scheme, the discrete part of a mixed input is shown to effectively behave as a common message in the sense that, although treated as noise, its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non-intended receiver. The practical implication is that a discrete interfering input is a friend, while an Gaussian interfering input is in general a foe. This paper also discusses other practical implications of the proposed TINnoTS scheme with mixed inputs. Since TINnoTS requires neither explicit joint decoding nor time sharing, the results of this paper are applicable to a variety of oblivious or asynchronous channels, such as the block asynchronous G-IC (which is not an information stable channel) and the G-IC with partial codebook knowledge at one or more receivers.Index Terms-Treating interference as noise, interference channel, discrete inputs.

Superposition Signaling in Broadcast Interference Networks

“…A similar result for the K-user cyclic GIN was obtained in [18]. It was also shown in [19]- [21] that using non-Gaussian inputs (or in [22] with Gaussian inputs) and treating interference as noise achieves the capacity region of some special SISO GINs within a constant gap. The withinconstant-gap results have a merit in the high signal-to-noise ratio (SNR) regime only, where the achievable rate region is sufficiently large.…”

A View of Information-Estimation Relations in Gaussian Networks

“…Another reason is that discrete inputs often outperform Gaussian inputs in competitive multi-user scenarios, such as the interference channel, as will be demonstrated in Section 7. For other examples of discrete inputs being useful in multi-user settings, the interested readers is referred to [43][44][45][46].…”

“…The bound depends only on the entropy, the LMMSE, and the minimum distance, which are usually easy to compute. The bound in (33) has also been proven to be useful for other problems such as two-user Gaussian interference channels [45,49], communication with a disturbance constraint [50], energy harvesting problems [51,52], and information-theoretic security [53].…”

“…This is enabled by using non-Gaussian inputs and designing the decoders that treat interference as noise by taking into account the correct (non-Gaussian) distribution of the interference. Such scenarios were considered in [44,46,49], and shown to be optimal to within either a constant or a O(log log(snr)) gap for all regimes in [45].…”

“…Because Gaussian inputs are often mutual information maximizers, one might think that the expression in (108) is the best that we can hope for. However, this intuition can be very misleading, and despite the simplicity of TIN, in [45] TINnoTS was shown to achieve capacity C within a gap which also implies that TIN is gDoF optimal. The key observation is to use non-Gaussian inputs, specifically the mixed inputs presented in Section 5.5.…”