Related papers: Attaining Capacity with Algebraic Geometry Codes t…
Given a probability distribution $\mathcal{D}$ over the non-negative integers, a $\mathcal{D}$-repeat channel acts on an input symbol by repeating it a number of times distributed as $\mathcal{D}$. For example, the binary deletion channel…
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated…
A fundamental problem in coding theory is the design of an efficient coding scheme that achieves the capacity of the additive white Gaussian (AWGN) channel. The main objective of this short note is to point out that by concatenating a…
We construct concatenated capacity-achieving quantum codes for noisy optical quantum channels. We demonstrate that the error-probability of capacity-achieving quantum polar encoding can be reduced by the proposed low-complexity…
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to…
The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied…
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the…
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 the low-energy high-energy-efficiency regime of classical optical communications---relevant to deep-space optical channels---there is a big gap between reliable communication rates achievable via conventional optical receivers and the…
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to…
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…
It is shown that polar codes achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the…
We propose to reduce the decoding complexity of polar codes with non-Arikan kernels by employing a (near) ML decoding algorithm for the codes generated by kernel rows. A generalization of the order statistics algorithm is presented for soft…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
Polar codes were introduced by Arikan in 2008 and are the first family of error-correcting codes achieving the symmetric capacity of an arbitrary binary-input discrete memoryless channel under low complexity encoding and using an efficient…
Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this…
The interpolation based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (ASD) further improves the decoding…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the analysis and construction of polar codes involve the complex iterative-calculation. In…