Related papers: Ratio List Decoding
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
We prove that Reed-Solomon (RS) codes with random evaluation points are list recoverable up to capacity with optimal output list size, for any input list size. Namely, given an input list size $\ell$, a designated rate $R$, and any…
This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
We study list-recoverability of random linear codes over small fields, both from errors and from erasures. We consider codes of rate $\epsilon$-close to capacity, and aim to bound the dependence of the output list size $L$ on $\epsilon$,…
We prove new upper bounds on the size of families of vectors in $\Z_m^n$ with restricted modular inner products, when $m$ is a large integer. More formally, if $\vec{u}_1,\ldots,\vec{u}_t \in \Z_m^n$ and $\vec{v}_1,\ldots,\vec{v}_t \in…
A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities,…
Folded Reed-Solomon (FRS) codes are a well-studied family of codes, known for achieving list decoding capacity. In this work, we give improved deterministic and randomized algorithms for list decoding FRS codes of rate $R$ up to radius…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
We analyze deterministic message identification via channels with non-discrete additive white noise and with a noiseless feedback link under both average power and peak power constraints. The identification task is part of Post Shannon…
The rapidly improving performance of modern hardware renders convolutional codes obsolete, and allows for the practical implementation of more sophisticated correction codes such as low density parity check (LDPC) and turbo codes (TC). Both…
A binary code Enc$:\{0,1\}^k \to \{0,1\}^n$ is $(0.5-\epsilon,L)$-list decodable if for all $w \in \{0,1\}^n$, the set List$(w)$ of all messages $m \in \{0,1\}^k$ such that the relative Hamming distance between Enc$(m)$ and $w$ is at most…
This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the…
In this paper, we study the coding delay and the average coding delay of random linear network codes (dense codes) over line networks with deterministic regular and Poisson transmission schedules. We consider both lossless networks and…
Following initial work by JaJa, Ahlswede and Cai, and inspired by a recent renewed surge in interest in deterministic identification (DI) via noisy channels, we consider the problem in its generality for memoryless channels with finite…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
Typical random codes (TRC) in a communication scenario of source coding with side information at the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random…
The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on…
In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order-$\ell$ MDS code, denoted by $\operatorname{MDS}(\ell)$, has the property that any $\ell$ subspaces formed from…