Related papers: A Note on Comparison of Error Correction Codes
In fact, the broadcast nature of every transmitter makes it possible for other transceivers in the channel to overhear the broadcasted signal. The proposed idea in cooperative communication is to use these intermediate transceivers as relay…
Bosonic codes with rotational symmetry are currently one of the best performing quantum error correcting codes. Little is known about error propagation and code distance for these rotation codes in contrast with qubit codes and Bosonic…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
Despite the effectiveness of large language models (LLMs) for code generation, they often output incorrect code. One reason is that model output probabilities are often not well-correlated with correctness, and reflect only the final output…
An information theoretic framework for unequal error protection is developed in terms of the exponential error bounds. The fundamental difference between the bit-wise and message-wise unequal error protection (UEP) is demonstrated, for…
A new approach to the problem of error correction in communication channels is proposed, in which the input sequence is transformed in such a way that the interdependence of symbols is significantly increased. Then, after the sequence is…
We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. The key idea is to define two systems, one modelling…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…
Derrida's model can be used for construction and transmission of error correcting codes, in an optimal way. we use the extreme statistics method to derive the optimal signal to noise ratio.
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
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,…
This paper investigates the performance of wireless systems that employ finite-blocklength channel codes for transmission and operate under queueing constraints in the form of limitations on buffer overflow probabilities. A block fading…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
With the rise of critical machine-to-machine applications, next generation wireless communication systems must be designed with strict constraints on the latency and reliability. A key question in this context relates to channel state…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
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…
A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Running the code with given values of the vector of inputs, x, leads to an output y(x) or several such outputs.…
This paper considers the queueing performance of a system that transmits coded data over a time-varying erasure channel. In our model, the queue length and channel state together form a Markov chain that depends on the system parameters.…