Writing on the Facade of RWTH ICT Cubes: Cost Constrained Geometric Huffman Coding

TL;DR

This paper introduces cost constrained Geometric Huffman coding (ccGhc), a novel method for encoding that minimizes divergence from a target distribution under cost constraints, with applications in architecture and communication channels.

Contribution

The paper develops ccGhc, a new coding technique that optimally balances cost constraints and information encoding, with proven asymptotic optimality and practical applications.

Findings

ccGhc matches architectural design criteria at blocklength 3

ccGhc efficiently finds capacity-achieving modulation codes

Asymptotic optimality proven for large blocklengths

Abstract

In this work, a coding technique called cost constrained Geometric Huffman coding (ccGhc) is developed. ccGhc minimizes the Kullback-Leibler distance between a dyadic probability mass function (pmf) and a target pmf subject to an affine inequality constraint. An analytical proof is given that when ccGhc is applied to blocks of symbols, the optimum is asymptotically achieved when the blocklength goes to infinity. The derivation of ccGhc is motivated by the problem of encoding a text to a sequence of slats subject to architectural design criteria. For the considered architectural problem, for a blocklength of 3, the codes found by ccGhc match the design criteria. For communications channels with average cost constraints, ccGhc can be used to efficiently find prefix-free modulation codes that are provably capacity achieving.