In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on LVFC bound. On the other hand, a class of constant composition codes is derived from known linear codes.
We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of simultaneously benefiting both from the probabilistic shaping of the channel input and from the linear structure of the code. We prove that the codebook mismatch can be fully compensated by using a mismatched additive decoding metric that achieves the random coding error exponent of (non-linear) constant composition codes. As the coding rate tends to the mutual infor…
Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have been selected as one of the coding schemes in the $5^{th}$ generation wireless standard (5G). Over the years various polar code decoding algorithms, like SC-list (SCL), have been proposed to improve the mediocre performance of the successive cancellation (SC) decoding algorithm for finite code lengths; however, like SC, they suffer from long decoding latency…
A basic problem for constant dimension codes is to determine the maximum possible size $A_q(n,d;k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$, called codewords, such that the subspace distance satisfies $d_S(U,W):=2k-2\dim(U\cap W)\ge d$ for all pairs of different codewords $U$, $W$. Constant dimension codes have applications in e.g.\ random linear network coding, cryptography, and distributed storage. Bounds for $A_q(n,d;k)$ are the topic of many recent research papers. Providing a general framework we survey many of the latest constructions and show up the potential for furth…
Supporting Information for the Paper: Optimal Ternary Constant-Composition Codes of Weight Four and Distance Five, IEEE Trans. Inform. Theory, To Appear
Envelopes of upper bounds for nonbinary constant-weight and constant-composition codes
Moscow Institute of Physics and Technology (State University)（莫斯科物理技术学院）；Institute of Mathematics and Informatics, Bulgarian Academy of Sciences（保加利亚科学院数学与信息学研究所）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）；Adyghe State University（阿迪格国立大学）
There are different inequivalent ways to define the Rényi capacity of a channel for a fixed input distribution $P$. In a 1995 paper Csiszár has shown that for classical discrete memoryless channels there is a distinguished such quantity that has an operational interpretation as a generalized cutoff rate for constant composition channel coding. We show that the analogous notion of Rényi capacity, defined in terms of the sandwiched quantum Rényi divergences, has the same operational interpretation in the strong converse problem of classical-quantum channel coding. Denoting the constant compositi…
In order to realize probabilistically shaped signaling within the probabilistic amplitude shaping (PAS) framework, a shaping device outputs sequences that follow a certain nonuniform distribution. In case of constant-composition (CC) distribution matching (CCDM), the sequences differ only in the ordering of their constituent symbols, whereas the number of occurrences of each symbol is constant in every output block. Recent results by Amari \textit{et al.} have shown that the CCDM block length can have a considerable impact on the effective signal-to-noise ratio (SNR) after fiber transmission. …
Optimal Ferrers Diagram Rank-Metric Codes: New Constructions, Diagram Combinations, and Applications to Constant-Dimension Subspace Codes
Chern Institute of Mathematics and LPMC, Nankai University（南开大学陈省身数学研究所和LPMC）；School of Cyberspace Security, Beijing University of Posts and Telecommunications（北京邮电大学网络空间安全学院）；Department of Mathematics, University of Paris VIII（巴黎第八大学数学系）；Laboratory Geometry, Analysis and Applications, LAGA, University Sorbonne Paris Nord, CNRS, UMR 7539（索邦巴黎北大学LAGA几何、分析与应用实验室）；Telecom Paris, Polytechnic Institute of Paris（巴黎综合理工学院巴黎电信学院）；College of Science, Civil Aviation University of China（中国民航大学理学院）
