Related papers: Optimal coding for the deletion channel with small…
Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion…
In the random deletion channel, each bit is deleted independently with probability $p$. For the random deletion channel, the existence of codes of rate $(1-p)/9$, and thus bounded away from $0$ for any $p < 1$, has been known. We give an…
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…
Synchronization channels, such as the well-known deletion channel, are surprisingly harder to analyze than memoryless channels, and they are a source of many fundamental problems in information theory and theoretical computer science. One…
We consider the source-channel separation architecture for lossy source coding in communication networks. It is shown that the separation approach is optimal in two general scenarios, and is approximately optimal in a third scenario. The…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
In this paper we show a polar coding scheme for the deletion channel with a probability of error that decays roughly like $2^{-\sqrt{\Lambda}}$, where $\Lambda$ is the length of the codeword. That is, the same decay rate as that of seminal…
In this paper, we introduce a new practical and general method for solving the main problem of designing the capacity approaching, optimal rate, irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC).…
We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been…
A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson…
The problem of reconstructing a source sequence with the presence of decoder side-information that is mis-synchronized to the source due to deletions is studied in a distributed source coding framework. Motivated by practical applications,…
Two of the most common models for channels with synchronisation errors are the Binary Deletion Channel with parameter $p$ ($\text{BDC}_p$) -- a channel where every bit of the codeword is deleted i.i.d with probability $p$, and the Poisson…
Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an…
A message composed of packets is transmitted using erasure and channel coding over a fading channel with no feedback. For this scenario, the paper explores the trade-off between the redundancies allocated to the packet-level erasure code…
This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter $p$ (BDC$_p$) every bit is deleted…
This paper considers a binary channel with deletions. We derive two close form upper bound on the capacity of binary deletion channel. The first upper bound is based on computing the capacity of an auxiliary channel and we show how the…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
This paper studies the problem of reconstructing a word given several of its noisy copies. This setup is motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm, a word is…
We develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information between the input and…
We present an optimized implementation of the Blahut-Arimoto algorithm via GPU parallelization, which we use to obtain improved upper bounds on the capacity of the binary deletion channel. In particular, our results imply that the capacity…