Stefano Della Fiore

Stefano Della Fiore

We derive refined entropy upper bounds for $q$-ary $B_2$ codes by exploiting the Fourier structure of the i.i.d. difference distribution $D=X-Y$. Since the pmf of $D$ is an autocorrelation, its Fourier series is a nonnegative trigonometric polynomial of degree at most $q-1$. This leads to a natural convex relaxation over candidate difference distributions, equivalently expressible through an infinite family of positive semidefinite Toeplitz constraints. The resulting formulation admits a simple Gram interpretation and yields certified upper bounds through truncated semidefinite programs. Combined with the prefix-suffix method, this gives improved asymptotic rate upper bounds for $q$-ary $B_2$ codes; in particular, for $q\in\{9,10,11,12,13\}$ the resulting values improve on the best bounds known in the literature. We also study binary constant-weight $B_2$ codes. Extending the distance-distribution method of Cohen, Litsyn, and Zémor to the constant-weight setting, and combining it with Litsyn's asymptotic linear-programming bound for constant-weight codes, we derive a new upper bound on the constant-weight $B_2$ rate.

Stefano Della Fiore, Alessandro Gnutti, Marco Dalai et al.

Traditional image compression methods aim to reconstruct images for human perception, prioritizing visual fidelity over task relevance. In contrast, Coding for Machines focuses on preserving information essential for automated understanding. Building on this principle, we present an end-to-end compression framework that retains text-specific features for Optical Character Recognition (OCR). The encoder operates at roughly half the computational cost of the OCR module, making it suitable for resource-limited devices. When on-device OCR is infeasible, images can be efficiently compressed and later decoded to recover textual content. Experiments show significant improvements in text extraction accuracy at low bitrates, even outperforming OCR on uncompressed images. We further extend this study to general-purpose encoders, exploring their capacity to preserve hidden semantics under extreme compression. Instead of optimizing for visual fidelity, we examine whether compact, visually degraded representations can retain recoverable meaning through learned enhancement and recognition modules. Results demonstrate that semantic information can persist despite severe compression, bridging text-oriented compression and general-purpose semantic preservation in machine-centered image coding.