# Unveiling Bias Compensation in Turbo-Based Algorithms for (Discrete) Compressed Sensing

## TL;DR

This paper explores turbo-based algorithms for discrete compressed sensing, revealing how bias compensation improves recovery of finite-valued sparse signals and providing a deeper understanding from a communications perspective.

## Contribution

It introduces an analysis of turbo algorithms for discrete compressed sensing, highlighting bias unbiasing and proposing an improved algorithm.

## Key findings

- Bias calculation equals unbiasing of biased estimates
- Improved turbo algorithm enhances discrete signal recovery
- Deeper understanding of algorithm behavior from communications perspective

## Abstract

In Compressed Sensing, a real-valued sparse vector has to be recovered from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. Adapted algorithms incorporating this additional knowledge are required for the discrete-valued setup. In this paper, turbo-based algorithms for both cases are elucidated and analyzed from a communications engineering perspective, leading to a deeper understanding of the algorithm. In particular, we gain the intriguing insight that the calculation of extrinsic values is equal to the unbiasing of a biased estimate and present an improved algorithm.