Modern communication systems increasingly employ probabilistic amplitude shaping (PAS) to close the gap to the Shannon capacity by generating non-uniform input distributions (typically approximating Maxwell–Boltzmann distributions). At the core of PAS lies the distribution matcher (DM), which maps uniformly distributed information bits into shaped sequences of amplitudes.

A central challenge is designing DMs that achieve low rate loss and low complexity.

Enumerative Sphere Shaping (ESS) addresses these challenges by restricting sequences to lie within a hypersphere in the energy domain. Instead of fixing symbol composition (as in CCDM), ESS selects sequences such that their total energy does not exceed a predefined radius. This approach results in competitive performance in the short blocklength regime.

The student will explore ESS [1][2], including its theoretical foundation in information and coding theory, algorithmic implementation, storage and computational complexity, and comparisons with other shaping methods such as CCDM and shell mapping [3]. 

[1] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8850066

[2] https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8895789&casa_token=sZch6uYNxusAAAAA:Oq9owJ8tNEA5puQv1Bai7enCei8nYMoPEwt9jO3q-9upB20dTKJPltXrbI7mPSKnsVs_nK_G

[3] https://www.mdpi.com/1099-4300/22/5/581

Prerequisites

 In this seminar, students will explore the Context Tree Weighting (CTW) method [1], a universal lossless technique for sequential data compression and prediction. CTW efficiently balances multiple context models using a weighted averaging approach. It is particularly appreciated for its strong theoretical guarantees, such as redundancy bounds in universal coding, while also demonstrating excellent practical performance in real-world scenarios.

Students will first read and understand the fundamentals of CTW, including its theoretical basis and algorithmic implementation. After grasping the core method, they can choose to delve into either extensions of CTW [2], or its applications, e.g. text/image compression [3, 4] or sequence prediction in various domains.

[1] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=382012

[2] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=661523

[3] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=838152

[4] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=488318

Prerequisites