Bounds on the Effective-length of Optimal Codes for Interference Channel with Feedback

TL;DR

This paper demonstrates that in interference channels with feedback, finite effective length codes are essential for optimal communication, challenging the notion that asymptotically large codes are always sufficient.

Contribution

It provides examples showing large effective length codes are sub-optimal in feedback channels, emphasizing the importance of finite effective length codes for optimality.

Findings

Finite effective length codes are necessary for optimality.

Large effective length codes can be sub-optimal in feedback channels.

Feedback enables correlation preservation, crucial for coordination.

Abstract

In this paper, we investigate the necessity of finite blocklength codes in distributed transmission of independent message sets over channels with feedback. Previously, it was shown that finite effective length codes are necessary in distributed transmission and compression of sources. We provide two examples of three user interference channels with feedback where codes with asymptotically large effective lengths are sub-optimal. As a result, we conclude that coded transmission using finite effective length codes is necessary to achieve optimality. We argue that the sub-optimal performance of large effective length codes is due to their inefficiency in preserving the correlation between the inputs to the distributed terminals in the communication system. This correlation is made available by the presence of feedback at the terminals and is used as a means for coordination between the terminals when using finite effective length coding strategies.