Related papers: Extended Unary Coding
The distributed index coding problem is studied, whereby multiple messages are stored at different servers to be broadcast to receivers with side information. First, the existing composite coding scheme is enhanced for the centralized…
Extended $1$-perfect codes in the Hamming scheme $H(n,q)$ can be equivalently defined as codes that turn to $1$-perfect codes after puncturing in any coordinate, as completely regular codes with certain intersection array, as uniformly…
This paper proposes an erasure correcting code and its systematic form for the distributed storage system. The proposed codes are encoded by exclusive OR and bit-level shift operation. By the shift operation, the encoded packets are…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
A code is called solid if, roughly speaking, any correctly-transmitted codeword in an arbitrarily corrupted string of codewords can still be decoded correctly and unambiguously. So-called variable-length solid codes, in which codewords may…
The number of random bits required to approximate a target distribution in terms of un-normalized informational divergence is considered. It is shown that for a variable-to-variable length encoder, this number is lower bounded by the…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer r > 1, there exist two…
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a numerically stable binary coding method which overcomes the drawbacks of the \textit{Fractional…
Concurrent coding is an unconventional encoding technique that simultaneously provides protection against noise, burst errors and interference. This simple-to-understand concept is investigated by distinguishing 2 types of code, open and…
We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.
A tapered floating point encoding is proposed which uses the redundant signed radix 2 system and is based on the canonical recoding. By making use of ternary technology, the encoding has a dynamic range exceeding that of the…
We generalize probabilistic amplitude shaping (PAS) with binary codes to the case of non-binary codes defined over prime finite fields. Firstly, we introduce probabilistic shaping via time sharing where shaping applies to information…
This paper introduces a new counting code. Its design was motivated by distributed video coding where, for decoding, error correction methods are applied to improve predictions. Those error corrections sometimes fail which results in…
A new family of sequences is proposed. An example of sequence of this family is more accurately studied. This sequence is composed by the integers $n$ for which the sum of binary digits is equal to the sum of binary digits of $n^2$. Some…
Recently, Byrnes presented a formula for the maximum length of a symmetric circuit code that has a long bit run and odd spread. Here we show that the formula is also valid when the spread is even. We also establish that all maximum length…
A new class of codes, Extended Product (EPC) Codes, consisting of a product code with a number of extra parities added, is presented and applications for erasure decoding are discussed. An upper bound on the minimum distance of EPC codes is…
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…
Spread codes and orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability and transmission rate, but the question of how to encode messages has not been…
The mean length and the variability of coding sequences for 48 genomes of bacteria and archaea were analyzed. It was found that the plotted data can be described by an angular area. This suggests the followings: a) The variability of a…