The strict delay constraints of real-time communication applications in packet networks limit the use of ARQ (retransmission systems) and error correction codes with extensive interleaving and decoding over long intervals. Since packet losses can introduce significant impairments, we study the effectiveness of low delay channel coding techniques to increase transmission quality across links wit...

Concatenated coding schemes were first proposed by Forney [1] as a method for achieving large coding gains by combining two or more relatively simple buildingblock or component codes (sometimes called constituent codes). The resulting codes had the error-correction capability of much longer codes, and they were endowed with a structure that permitted relatively easy to moderately complex decodi...

The turbo decoding algorithm of a decade ago constituted a milestone in error-correction coding for digital communications, and has inspired extensions to generalized receiver topologies, including turbo equalization, turbo synchronization, and turbo CDMA, among others. Despite an accrued understanding of iterative decoding over the years, the “turbo principle” remains elusive to master analyti...

This paper introduces multidimensional generalizations of binary Reed–Muller codes where the codewords are projection operators, and the corresponding subspaces are widely separated with respect to the chordal distance on Grassmannian space. Parameters of these Grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for bi...

We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and characterize the performance of both a repetition code and an error avoiding code (CRC and CDFS, respectively) in terms of the entanglement fidelity. We also c...

Recently [1] we proposed a family of magic state distillation protocols that obtains asymptotic performance that is conjectured to be optimal. This family depends upon several codes, called “inner codes” and “outer codes.” In Ref. 1, some small examples of these codes were given as well as an analysis of codes in the asymptotic limit. Here, we analyze such protocols in an intermediate size regi...

We study a quantum analogue of locally decodable error-correcting codes. A q-query locally decodable quantum code encodes n classical bits in an m-qubit state, in such a way that each of the encoded bits can be recovered with high probability by a measurement on at most q qubits of the quantum code, even if a constant fraction of its qubits have been corrupted adversarially. We show that such a...

A code-division multiple-access system with channel coding may be viewed as a serially-concatenated coded system. In this paper we propose a low complexity method for decoding the resulting inner code (due to the spreading sequence), which allows iterative (turbo) decoding of the serially-concatenated code pair. The per-bit complexity of the proposed decoder increases only linearly with the num...

A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n, k, d]] = [[2r, 2r −C(r, t)− 2 ∑t−1 i=0 C(r, i), 2 t + 2t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical information theory have counterparts in quantum information theory, and among these is the idea of a...

This paper describes an experimental new link layer protocol for amateur packet radio use. It extends my earlier MACA scheme for dealing with hidden terminals by incorporating a powerful forward error correction (FEC) scheme: convolutional coding with sequential decoding. The resulting hybrid protocol combines the best of the FEC and retransmission (ARQ) techniques. It should perform very well ...