Related papers: New model for rigorous analysis of LT-codes
For a layered probabilistic shaping (PS) scheme with a general decoding metric, an achievable rate is derived using Gallager's error exponent approach and the concept of achievable code rates is introduced. Several instances for specific…
Undetected errors are important for linear codes, which are the only type of errors after hard decision and automatic-repeat-request (ARQ), but do not receive much attention on their correction. In concatenated channel coding, suboptimal…
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Suppose that we have two training sequences generated by parametrized distributions $P_{\theta^*}$ and $P_{\xi^*}$, where $\theta^*$ and $\xi^*$ are unknown true parameters. Given training sequences, we study the problem of classifying…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
Raptor codes have been widely used in many multimedia broadcast/multicast applications. However, our understanding of Raptor codes is still incomplete due to the insufficient amount of theoretical work on the performance analysis of Raptor…
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
The recently proposed SCLF decoding algorithm for polar codes improves the error-correcting performance of state-of-the-art SCL decoding. However, it comes at the cost of a higher complexity. In this paper, partitioned polar codes tailored…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
We define the error exponent of the typical random code as the long-block limit of the negative normalized expectation of the logarithm of the error probability of the random code, as opposed to the traditional random coding error exponent,…
A rate-dependent upper bound of the best achievable block error probability of polar codes with successive-cancellation decoding is derived.
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
Transformer-based autoregressive sampling has been the major bottleneck for slowing down large language model inferences. One effective way to accelerate inference is \emph{Speculative Decoding}, which employs a small model to sample a…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
One of the fundamental challenges in enabling fault-tolerant quantum computation is realising fast enough quantum decoders. We present a new two-stage decoder that accelerates the decoding cycle and boosts accuracy. In the first stage, a…
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded…
Obtaining high-quality outputs from Large Language Models (LLMs) often depends upon the choice of a sampling-based decoding strategy to probabilistically choose the next token at each generation step. While a variety of such sampling…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
We consider a single-source, multiple-relay, single-destination lossy network employing Random Linear Network coding at all transmitting nodes. We address the problem of calculating the probability of successful decoding at the destination…