Related papers: Parameters of Codes for the Binary Asymmetric Chan…
Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…
We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…
For information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that feedback…
This paper considers a binary channel with deletions. We derive two close form upper bound on the capacity of binary deletion channel. The first upper bound is based on computing the capacity of an auxiliary channel and we show how the…
Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Monomial codes were recently equipped with partial order relations, fact that allowed researchers to discover structural properties and efficient algorithm for constructing polar codes. Here, we refine the existing order relations in the…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
In this paper, we present a novel way for solving the main problem of designing the capacity approaching irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). The proposed method is much simpler, faster,…
A challenging problem related to the design of polar codes is "robustness against channel parameter variations" as stated in Ar{\i}kan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as…
Recently, quantum error-correcting codes were proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit flip and phase flip errors. An example for a channel which…
This paper focuses on finite-dimensional upper and lower bounds on decodable thresholds of Zm and binary low-density parity-check (LDPC) codes, assuming belief propagation decoding on memoryless channels. A concrete framework is presented,…
In digital systems such as fiber optical communications, the ratio between probability of errors of type $1\to 0$ and $0 \to 1$ can be large. Practically, one can assume that only one type of error can occur. These errors arecalled…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
Binary code similarity detection is to detect the similarity of code at binary (assembly) level without source code. Existing works have their limitations when dealing with mutated binary code generated by different compiling options. In…
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…