Related papers: Capacity Achieving Linear Codes with Random Binary…
In this paper, we establish the list-decoding capacity theorem for sum-rank metric codes. This theorem implies the list-decodability theorem for random general sum-rank metric codes: Any random general sum-rank metric code with a rate not…
In the application of linear network coding to wireless broadcasting with feedback, we prove that the problem of determining the existence of an innovative encoding vector is NP-complete when the finite field size is two. When the finite…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…
We study sparse regression codes (SPARC) for multiple access channels with multiple receive antennas, in non-coherent flat fading channels. We propose a novel practical decoder, referred to as maximum likelihood matching pursuit (MLMP),…
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…
A natural hypothesis for the success of reservoir computing in generic tasks is the ability of the untrained reservoir to map different input time series to separable reservoir states - a property we term separation capacity. We provide a…
We study a problem of constructing codes that transform a channel with high bit error rate (BER) into one with low BER (at the expense of rate). Our focus is on obtaining codes with smooth ("graceful") input-output BER curves (as opposed to…
Developing computationally-efficient codes that approach the Shannon-theoretic limits for communication and compression has long been one of the major goals of information and coding theory. There have been significant advances towards this…
We show that Gallager's ensemble of Low-Density Parity Check (LDPC) codes achieves list-decoding capacity with high probability. These are the first graph-based codes shown to have this property. This result opens up a potential avenue…
We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a…
We study codes on graphs combined with an iterative message passing algorithm for quantization. Specifically, we consider the binary erasure quantization (BEQ) problem which is the dual of the binary erasure channel (BEC) coding problem. We…
This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless…
We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $ P $ and $ N $…
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 $\epsilon$,…
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…
We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be…
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacityachieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures…
We study a problem of constructing codes that transform a channel with high bit error rate (BER) into one with low BER (at the expense of rate). Our focus is on obtaining codes with smooth ("graceful'') input-output BER curves (as opposed…
For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design,…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…