Related papers: Optimal Binary Variable-Length Codes with a Bounde…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
Huffman Codes are optimal Instantaneous Fixed-to-Variable (FV) codes in which every source symbol can only be encoded by one codeword. Relaxing these constraints permits constructing better FV codes. More specifically, recent work has shown…
A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the…
Certain binary asymmetric channels, such as Z-channels in which one of the two crossover probabilities is zero, demand optimal ones densities different from 50%. Some broadcast channels, such as broadcast binary symmetric channels (BBSC)…
We construct an optimal quantum universal variable-length code that achieves the admissible minimum rate, i.e., our code is used for any probability distribution of quantum states. Its probability of exceeding the admissible minimum rate…
In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood decoding are derived for different (nonbinary) Raptor code constructions. In particular four different constructions are considered; (i)…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we…
The maximum size $A_2(8,6;4)$ of a binary subspace code of packet length $v=8$, minimum subspace distance $d=6$, and constant dimension $k=4$ is $257$, where the $2$ isomorphism types are extended lifted maximum rank distance codes. In…
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…
This letter investigates a new class of index coding problems. One sender broadcasts packets to multiple users, each desiring a subset, by exploiting prior knowledge of linear combinations of packets. We refer to this class of problems as…
Linear complementary dual (LCD) codes can provide an optimum linear coding solution for the two-user binary adder channel. LCD codes also can be used to against side-channel attacks and fault non-invasive attacks. Let $d_{LCD}(n, k)$ denote…
This paper describes a search algorithm to find multiple sets of one dimensional unipolar (optical) orthogonal codes characterized by parameters, binary code sequence of length (n bits) and weight w (number of bit 1s in the sequence) as…
We propose almost instantaneous fixed-to-variable-length (AIFV) codes such that two (resp. $K-1$) code trees are used if code symbols are binary (resp. $K$-ary for $K \geq 3$), and source symbols are assigned to incomplete internal nodes in…
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…
In this paper, a virus optimization algorithm, which is one of the metaheuristic optimization technique, is employed for the first time to the problem of finding extremal binary self-dual codes. We present a number of generator matrices of…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
A binary code of blocklength $n$ and codebook size $M$ is called an $(n,M)$ code, which is studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood (ML) decoding. For any $n \geq 2$, some optimal codes among the…