arXiv subjects

Frederik Ritter

Publications and source records attributed to Frederik Ritter.

3 recordsLinked to original sources

arXiv2025

An Extension of Enumerative Sphere Shaping for Arbitrary Channel Input Distributions

A non-uniform channel input distribution is key for achieving the capacity of arbitrary channels. However, message bits are generally assumed to follow a uniform distribution which must first be transformed to a non-uniform distribution by using a distribution matching algorithm. One such algorithm is enumerative sphere shaping (ESS). Compared to algorithms such as constant composition distribution matching (CCDM), ESS can utilize more channel input symbol sequences, allowing it to achieve a comparably low rate loss. However, the distribution of channel input symbols produced by ESS is fixed, restricting the utility of ESS to channels with Gaussian-like capacity-achieving input distributions. In this paper, we generalize ESS to produce arbitrary discrete channel input distributions, making it usable on most channels. Crucially, our generalization replaces fixed weights used internally by ESS with weights depending on the desired channel input distribution. We present numerical simulations using generalized ESS with probabilistic amplitude shaping (PAS) to transmit sequences of 256 symbols over a simplified model of an unamplified coherent optical link, a channel with a distinctly non-Gaussian capacity-achieving input distribution. In these simulations, we found that generalized ESS improves the maximum transmission rate by 0.0425 bit/symbol at a frame error rate below 10^{-4} compared to CCDM.

cs.IT↗

arXiv2025

Removal of Small Weight Stopping Sets for Asynchronous Unsourced Multiple Access

In this paper, we analyze the formation of small stopping sets in joint factor graphs describing a frame-asynchronous two-user transmission. Furthermore, we propose an algorithm to completely avoid small stopping sets in the joint factor graph over the entire range of symbol delays. The error floor caused by these stopping sets is completely mitigated. Our key observation is that, while the order of bits in the codeword is irrelevant in a single-user environment, it turns out to be crucial in an asynchronous, unsourced two-user system. Subsequently, our algorithm finds a reordering of variable nodes which avoids the smallest stopping set in the joint graph. We show that further improvements can be achieved when girth optimization of the single-user graphs by progressive edge growth (PEG) is used in combination with our proposed algorithm. Starting with a randomized code construction with optimized degree distribution, our simulation results show that PEG followed by the proposed algorithm can improve the average per user probability of error in a noiseless channel by almost two orders of magnitude for a broad range of frame delays.

cs.IT↗

arXiv2024

Introducing RSESS: An Open Source Enumerative Sphere Shaping Implementation Coded in Rust

In this work, we present an open-source implementation of the enumerative sphere shaping (ESS) algorithm used for probabilistic constellation shaping (PCS). PCS aims at closing the shaping gap caused by using uniformly distributed modulation symbols in channels for which information theory shows non-uniformly distributed signaling to be optimal. ESS is one such PCS algorithm that sets itself apart as it operates on a trellis representation of a subset of the possible symbol sequences. ESS leads to an empirical distribution of the symbols that closely approximates the optimal distribution for the additive white Gaussian noise (AWGN) channel. We provide an open-source implementation of this algorithm in the compiled language Rust, as well as Python bindings with which our Rust code can be called in a regular Python script. We also compare simulation results on the AWGN channel using our implementation with previous works on this topic.

cs.IT↗