Related papers: Error Correcting Coding for a Non-symmetric Ternar…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary…
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…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
Consider a binary linear code of length $N$, minimum distance $d_{\text{min}}$, transmission over the binary erasure channel with parameter $0 < \epsilon < 1$ or the binary symmetric channel with parameter $0 < \epsilon < \frac12$, and…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar…
To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The…
We consider a relay channel for which the following assumptions are made. (1) The source-destination and relay-destination channels are orthogonal (frequency division relay channel). (2) The relay implements the decode-and-forward protocol.…
This work considers optimizing LDPC codes in the physical-layer network coded two-way relay channel using noncoherent FSK modulation. The error-rate performance of channel decoding at the relay node during the multiple-access phase was…
Channel coding alone is not sufficient to reliably transmit a message of finite length $K$ from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure…
Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
This paper provides novel insights into channel and subspace codes in nonadaptive channel sensing with a single RF chain. Observing that this problem naturally maps to a noncoherent decoding problem, we show that the sensing performance of…
We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of…