In this paper, we investigate the undetected error probabilities for bounded-distance decoding of binary primitive BCH codes when they are used for both error correction and detection on a binary symmetric channel. We show that the undetected error probability of binary linear codes can be quite simplified and quantified if weight distribution of the code is binomial-like. We obtain bounds on t...

We are interested in a function f(p) that represents the probability that a random subset of edges of a-regular graph G contains half the edges of some cycle of G. f(p) is also the probability that a codeword be corrupted beyond recognition when words of the cycle code of G are submitted to the binary symmetric channel. We derive a precise upperbound on the largest p for which f(p) can vanish w...

In recent years, content identification based on digital fingerprinting attracts a lot of attention in different emerging applications. In this paper, we perform the information–theoretic analysis of finite length digital fingerprinting systems. We show that the identification capacity over the Binary Symmetric Channel (BSC) is achievable by using Bounded Distance Decoder (BDD).

A much simpler proof of Theorem 1 from [1] is presented below, using notation and formulas numeration of [1]. The text below replaces the subsection General case from §4 of [1, p. 11]. General case. In the general case for some ω we are interested in a pairs (xi,xj) with dij = ωn. But there may exist a pairs (xk,xl) with dkl < ωn. Using the “cleaning” procedure [2] we show that the influence of...

For a class C of binary linear codes, we write θC : (0, 1) → [0, 12 ] for the maximum-likelihood decoding threshold function of C, the function whose value at R ∈ (0, 1) is the largest bit-error rate p that codes in C can tolerate with a negligible probability of maximum-likelihood decoding error across a binary symmetric channel. We show that, if C is the class of cycle codes of graphs, then θ...

Absfracf -Consider a broadcast network of N + 1 nodes in which each binary digit transmitted by each node is received by each other node via a binary symmetric channel of given transition probability. The errors on these channels are independent over transmitters, receivers, and time. Each node has a binary state, and the problem is to construct a distributed algorithm to find the parity of the...

In this paper we study the eeects of transmission noise on xed-length coded wavelet coee-cients. We extend our previous work on maximum a posteriori detectors 1] to include inter-bitplane information and determine which transmitted codeword was most likely corrupted into a received erroneous codeword. We present a simple method of recovering from these errors once detected and demonstrate our r...

In the paper notation from [1] is used. A binary symmetric channel (BSC) with crossover probability 0 < p < 1/2 and q = 1 − p is considered. Let F n denote the set of all 2 binary n-tuples, and d(x,y), x,y ∈ F n denote the Hamming distance between x and y. A subset C = C(M,n) = {x1, . . . ,xM} ⊆ F n is called a code of length n and cardinality M . The minimum distance of the code C is d(C) = mi...

In this article, we focus on the Balanced Scorecard (BSC) as a discursive practice. Instead of asking whether the figures in the BSC correspond to reality, or whether they serve the users’ purposes and behave according to their intentions, we have chosen to analyse how the BSC partakes in shaping the world it is intended to reflect. Two case studies will be presented in order to demonstrate how...

. • They are called fair since it is constructed by an equal number of all possible such columns (the number is called L). • Each fair code can be constructed by duplicating C (M,L) fair many times. • The fair weak flip codes have a maximum minimum Hamming distance and achieve the Plotkin bound. • These codes are not optimal in the sense of average error probability over the binary symmetric ch...