Information Loss due to Finite Block Length in a Gaussian Line Network: An Improved Bound

TL;DR

This paper derives an improved fundamental bound on the maximum information transmission rate in a Gaussian line network with finite block length, considering network size, power constraints, and noise.

Contribution

It introduces a new bound that explicitly accounts for finite block length effects in Gaussian cascade networks, improving upon previous bounds.

Findings

The bound depends only on network size, block length, rate, and SNR.

It provides a tighter limit on information transmission rates.

The bound is applicable to networks with arbitrary encoding/decoding at intermediate nodes.

Abstract

A bound on the maximum information transmission rate through a cascade of Gaussian links is presented. The network model consists of a source node attempting to send a message drawn from a finite alphabet to a sink, through a cascade of Additive White Gaussian Noise links each having an input power constraint. Intermediate nodes are allowed to perform arbitrary encoding/decoding operations, but the block length and the encoding rate are fixed. The bound presented in this paper is fundamental and depends only on the design parameters namely, the network size, block length, transmission rate, and signal-to-noise ratio.