Related papers: The Error Probability of Maximum-Likelihood Decodi…
We consider a molecular channel, in which messages are encoded to the frequency of objects in a pool, and whose output during reading time is a noisy version of the input frequencies, as obtained by sampling with replacement from the pool.…
A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism…
Top-$k$ decoding is a widely used method for sampling from LLMs: at each token, only the largest $k$ next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-$k$ and other sampling…
The likelihood decoder is a stochastic decoder that selects the decoded message at random, using the posterior distribution of the true underlying message given the channel output. In this work, we study a generalized version of this…
This dissertation focuses on fountain codes under maximum likelihood (ML) decoding. First LT codes are considered under a practical and widely used ML decoding algorithm known as inactivation decoding. Different analysis techniques are…
In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…
In this paper we study the decoding capabilities of convolutional codes over the erasure channel. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming…
This paper is concerned with the problem of error-free communication over the i.i.d. duplication channel which acts on a transmitted sequence $ x_1 \cdots x_n $ by inserting a random number of copies of each symbol $ x_i $ next to the…
We consider a variant of the channel simulation problem with a single input and multiple outputs, where Alice observes a probability distribution $P$ from a set of prescribed probability distributions $\mathbb{\mathcal{P}}$, and sends a…
We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors.…
K.A.S. Immink and J.H. Weber recently defined and studied a channel with both gain and offset mismatch, modelling the behaviour of charge-leakage in flash memory. They proposed a decoding measure for this channel based on minimising Pearson…
Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple…
The sequence reconstruction problem involves a model where a sequence is transmitted over several identical channels. This model investigates the minimum number of channels required for the unique reconstruction of the transmitted sequence.…
We consider the problem of joint source and channel coding of structured data such as natural language over a noisy channel. The typical approach to this problem in both theory and practice involves performing source coding to first…
Since the classical work of Berlekamp, McEliece and van Tilborg, it is well known that the problem of exact maximum-likelihood (ML) decoding of general linear codes is NP-hard. In this paper, we show that exact ML decoding of a classs of…
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly…
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our…