相关论文: A Note on the Injection Distance

A new lower bound on the error probability of maximum likelihood decoding of a binary code on a binary symmetric channel was proved in Barg and McGregor (2004, cs.IT/0407011). It was observed in that paper that this bound leads to a new…

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…

Quantum key distribution (QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most…

With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance…

This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a non-vanishing probability of error. The output distribution induced by an…

A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…

We consider a joint source channel coding (JSCC) problem in which we desire to transmit an arbitrary memoryless source over an arbitrary additive channel. We propose a mismatched coding architecture that consists of Gaussian codebooks for…

We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…

Insertion-deletion codes (insdel codes for short) play an important role in synchronization error correction. The higher the minimum insdel distance, the more insdel errors the code can correct. Haeupler and Shahrasbi established the…

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…

We consider the problem of information embedding where the encoder modifies a white Gaussian host signal in a power-constrained manner to encode the message, and the decoder recovers both the embedded message and the modified host signal.…

Despite the theoretical and practical significance of BCH codes, the exact minimum distance and dimension remain unknown for many families. This paper establishes the precise minimum distance and dimension of narrow-sense BCH codes $\C_{(q,…

We review three vector encodings of Bayesian network structures. The first one has recently been applied by Jaakkola 2010, the other two use special integral vectors formerly introduced, called imsets [Studeny 2005, Studeny 2010]. The…

Feedback holds a pivotal role in practical communication schemes, even though it does not enhance channel capacity. Its main attribute includes adaptability in transmission that allows for a higher rate of convergence of the error…

This paper studies the third-order characteristic of nonsingular discrete memoryless channels and the Gaussian channel with a maximal-power constraint. The third-order term in our expansions employs a new quantity here called the channel…

Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…

A flag is a sequence of nested subspaces of a given ambient space F_q^n over a finite field F_q. In network coding, a flag code is a set of flags, all of them with the same sequence of dimensions, the type vector. In this paper, we…

Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are…

The Knill-Laflamme (KL) conditions distinguish exact quantum error correction codes, and it has played a critical role in the discovery of state-of-the-art codes. However, the family of exact codes is a very restrictive one and does not…

After a discussion of the Griesmer and Heller bound for the distance of a convolutional code we present several codes with various parameters, over various fields, and meeting the given distance bounds. Moreover, the Griesmer bound is used…