communication protocol developers

Abstract: Random access codes (RACs) encode a $q$-ary input string into fewer $q$-ary symbols while allowing any requested input symbol to be recovered with probability above the random-guessing value $1/q$. However, it remains unclear what asymptotic guarantees on compression and recovery probability should be required of RACs. We address this question by introducing the notion of asymptotically good RACs and give two polynomial-time constructions. First, an $[n,k,d]_q$ linear code with $d\ge2$, together with an encoder based on its orthogonal-array property, yields an $(n,n-k)_q$-RAC with worst-case decoding success probability \[ p_{\rm wc}=\frac{1}{q}+\left(1-\frac{1}{q}\right)\frac{d-2}{n}. \] These OA-RACs are asymptotically good whenever the underlying linear codes are, and Garcia--Stichtenoth algebraic-geometry codes give a concrete polynomial-time realization. Second, a direct-sum strategy using OA-RACs derived from $q$-ary Hamming codes and the trivial $(1,1)_q$-RAC yields asymptotically good RAC families at every prescribed RAC rate $R_{\rm RAC}=(n-k)/n\in(0,1)$. Numerical results demonstrate favorable finite-length performance of both constructions.

Abstract: This paper considers reliable in-sequence molecular communication, where bio-nanomachines exchange molecule-encoded information in a specified order, and investigates a new simulation-based method to incrementally evaluate communication protocols by gradually increasing the complexity of experimental settings. The proposed method, called Affine Memory Replay (AMR), builds a continual learning (CL) model to estimate communication performance between bio-nanomachines. AMR stores past simulation samples and synthesizes additional replay samples through interpolation and extrapolation between past samples. Through incremental performance estimation tasks, it replays both past and synthetic samples to regularize model updates, helping the model adapt to new experimental settings while retaining knowledge from earlier ones. Experimental results show that AMR significantly outperforms existing CL methods in maintaining overall estimation accuracy across sequentially learned estimation tasks. It effectively balances memory stability and learning plasticity under moderate training cost.

Abstract: Function-correcting codes are designed to protect the function values of a prescribed function against errors. Every error-correcting code that provides data protection inherently offers some degree of protection for functions defined on the data. In this work, we introduce a class of codes over $\mathbb{Z}_m$, termed function-correcting Lee metric codes with data protection (FCLMCs with data protection), which simultaneously provide error protection for both the data and the corresponding function values under the Lee metric. We consider codes that provide protection against a prescribed level of error for the function values that exceeds the level of protection guaranteed for the underlying data. We present a general construction of these codes and derive lower and upper bounds on the optimal redundancy, including a Plotkin-type lower bound. Furthermore, we derive explicit upper bounds on the redundancy of FCLMCs with data protection for several important classes of functions, including locally binary Lee functions, the Lee weight function, and the modular sum function. Finally, since the Lee metric coincides with the Hamming metric over $\mathbb{Z}_2$, all of our results remain valid over $\mathbb{Z}_2$ with respect to the Hamming metric.

Abstract: We study peeling decoding on the binary erasure channel when redundant parity checks may be added without restriction in number, but each check is subject to a row-weight constraint. For random simple binary regular low-density parity-check (LDPC) codes, we consider the parity-check matrix formed by all nonzero dual codewords up to a prescribed weight. We show that, throughout an explicit logarithmic row-weight range, this complete family of redundant checks has the same asymptotic normalized-residual threshold as peeling with the original LDPC matrix. In the same range, with probability tending to one over the random code, it still has a linear-size stopping set that is uniquely decodable. Consequently, every parity-check representation whose peeling decoder succeeds on every uniquely decodable erasure pattern must contain checks above this logarithmic scale, and the supports of those heavier checks must collectively contain a linear number of coordinates. Thus row weight remains an asymptotic limitation even when the number and selection of redundant checks are unrestricted.

Abstract: Universal coding of integers (UCI) provides binary codewords for positive integers such that, for every nonincreasing source distribution $P$, the average codeword length stays within $K$ times $\max\{1,H(P)\}$. The smallest constant $K$ is called the minimum expansion factor of UCI $\mathcal{C}$, denoted $C_{\mathcal{C}}^{*}$. The optimal minimum expansion factor $C^*=\inf\{C_{\mathcal{C}}^{*}\}$ is the minimum expansion factor corresponding to the optimal UCI. The optimal minimum expansion factor is currently known to lie in the range $2\le C^*\le 2.0386$. In this paper, we construct a family of one-point plus uniform-tail distributions and prove that, for every universal code, the worst-case ratio is attained by a distribution in this family, so that the family is least favorable for the UCI problem. We further establish an inequality, called the \emph{UCI inequality}, which plays the same role for UCI as the Kraft inequality does for prefix codes: for any real number $B$, it decides whether $B$ lies below or above $C^*$. Through the UCI inequality, we obtain an equivalent definition of $C^*$. By numerical computation, we determine $C^*=2.000124757036101\cdots$, the first fifteen decimal digits being certified. Once $C^*$ is known, we can theoretically construct the optimal UCI.

Abstract: Experiments have shown that modifications in communication hardware can enable unauthorized exfiltration of data from transmitters. We study the resulting Transmitter Trojan channel, in which a malicious encoder embedded within a legitimate transmitter perturbs the transmitted codeword on a symbol-by-symbol basis. The model reflects the limited footprint, delay, and computational complexity available to such hardware modifications. We derive achievable rogue message rate and achievable rates for the legitimate message under the mismatch induced by the Trojan. We also analyze decoding error exponents for the legitimate and rogue receivers, including operational exponent lower bounds obtained through channel-resolvability transfer arguments. Finally, we study Trojan detection at the legitimate receiver under different levels of statistical knowledge, including likelihood-ratio detection when the ensemble-averaged induced channel is known and goodness-of-fit detection when only the nominal channel is known. The resulting detection error exponents, together with the achievable rate and decoding error exponents, quantify tradeoffs among rogue message rate, legitimate message rate, decoding reliability, and Trojan detectability. We specialize the analysis to the binary symmetric channel and the additive white Gaussian noise channel, and illustrate the resulting tradeoffs numerically.