Related papers: Efficient Near-Optimal Codes for General Repeat Ch…
We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the…
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…
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…
The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Input bits are deleted independently with probability d, and when they are not deleted, they are not affected by the channel.…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. However, algorithms that encode exact samples usually have…
Transmission of information reliably and efficiently across channels is one of the fundamental goals of coding and information theory. In this respect, efficiently decodable deterministic coding schemes which achieve capacity provably have…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate…
This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…
We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
In this paper we show how to attain the capacity of discrete symmetric channels with polynomial time decoding complexity by considering iterated $(U|U+V)$ constructions with Reed-Solomon code or algebraic geometry code components. These…
We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback…
Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding have become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT) networks. To this end,…
Channels with synchronization errors, exhibiting deletion and insertion errors, find practical applications in DNA storage, data reconstruction, and various other domains. Presence of insertions and deletions render the channel with memory,…
We provide $poly\log$ sparse quantum codes for correcting the erasure channel arbitrarily close to the capacity. Specifically, we provide $[[n, k, d]]$ quantum stabilizer codes that correct for the erasure channel arbitrarily close to the…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…