Related papers: Explicit Capacity-achieving Codes for Worst-Case A…
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…
In this study we consider rateless coding over discrete memoryless channels (DMC) with feedback. Unlike traditional fixed-rate codes, in rateless codes each codeword is infinitely long, and the decoding time depends on the confidence level…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
A random access code (RAC) encodes an $L$-bit string into a $k$-bit message, where $L>k$, such that any requested bit can be decoded with high probability; a quantum RAC (QRAC) replaces the message with $k$ qubits. This paper provides a…
Sparse superposition codes, or sparse regression codes (SPARCs), are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…
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…
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…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error…
This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single…
We consider transmission over a binary-input additive white Gaussian noise channel using low-density parity-check codes. One of the most popular techniques for decoding low-density parity-check codes is the linear programming decoder. In…
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over…
In this paper we study codes for correcting deletable errors in binary words, where each bit is either retained, substituted, erased or deleted and the total number of errors is much smaller compared to the length of the codeword. We…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
We present a method of constructing rate-compatible polar codes that are capacity-achieving with low-complexity sequential decoders. The proposed code construction allows for incremental retransmissions at different rates in order to adapt…
While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…
We consider the zero-error capacity of deletion channels. Specifically, we consider the setting where we choose a codebook ${\cal C}$ consisting of strings of $n$ bits, and our model of the channel corresponds to an adversary who may delete…