Related papers: Algorithmic Polarization for Hidden Markov Models
Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel…
We consider the problem of joint source and channel coding of structured data such as natural language over a noisy channel. The typical approach to this problem in both theory and practice involves performing source coding to first…
The channel polarization behavior of polar codes under noise with memory is investigated. By introducing a genie-aided channel model, we first show that the polarized subchannels still converge to extremal channels under the standard polar…
For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall…
We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances…
In distributed optimization and machine learning, multiple nodes coordinate to solve large problems. To do this, the nodes need to compress important algorithm information to bits so that it can be communicated over a digital channel. The…
As the use of Internet of Things (IoT) devices for monitoring purposes becomes ubiquitous, the efficiency of sensor communication is a major issue for the modern Internet. Channel coding is less efficient for extremely short packets, and…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…
Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an…
Source polar coding is a potential solution for short blocklength-based low-latency key generation with limited sources, which is a critical aspect of six generation (6G) Internet of things. However, existing source coding schemes still…
We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching…
This paper first presents a new approach to evaluating the descriptive complexity of finite-length binary sequences. Specifically, we investigate the sequence-wise recovery behavior induced by polar compression and successive cancellation…
Polar coding is a method for communication over noisy classical channels which is provably capacity-achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information…
Polar codes, introduced recently by Ar\i kan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation,…
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…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from…
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…
In 2008 Arikan proposed polar coding [arXiv:0807.3917] which we summarize as follows: (a) From the root channel $W$ synthesize recursively a series of channels $W_N^{(1)},\dotsc,W_N^{(N)}$. (b) Select sophisticatedly a subset $A$ of…