Related papers: On the Pseudocodeword Redundancy
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…
Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association…
In this paper we focus our attention on a family of finite geometry codes, called type-I projective geometry low-density parity-check (PG-LDPC) codes, that are constructed based on the projective planes PG{2,q). In particular, we study…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
Function-correcting codes, introduced by Lenz, Bitar, Wachter-Zeh, and Yaakobi, protect specific function values of a message rather than the entire message. A central challenge is determining the optimal redundancy -- the minimum…
Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed redundancy $ r $,…
We present a framework for minimizing costs in constant weight codes while maintaining a certain amount of differentiable codewords. Our calculations are based on a combinatorial view of constant weight codes and relay on simple…
Consider a linear [n,k,d]_q code C. We say that that i-th coordinate of C has locality r, if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small…
We present lower bounds on the minimum pseudocodeword effective Euclidean distance (or minimum "pseudodistance") for coded modulation systems using linear codes with $q$-ary phase-shift keying (PSK) modulation over the additive white…
We use a simple construction called `recursive subproducts' (that is known to yield good codes of lengths $n^m$, $n \geq 3$) to identify a family of codes sandwiched between first-order and second-order Reed-Muller (RM) codes. These codes…
Four different ways of obtaining low-density parity-check codes from expander graphs are considered. For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived.…
Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of…
Function-correcting codes (FCCs) protect specific function evaluations of a message against errors. This condition imposes a less stringent distance requirement than classical error-correcting codes (ECCs), allowing for reduced redundancy.…
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…
In this paper we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of…
A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise…
Let At denote the set of infinite sequences of effective dimension t. We determine both how close and how far an infinite sequence of dimension s can be from one of dimension t, measured using the Besicovitch pseudometric. We also identify…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…
Let C be a linear code with length n and minimum distance d. The stopping redundancy of C is defined as the minimum number of rows in a parity-check matrix for C such that the smallest stopping sets in the corresponding Tanner graph have…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…