Related papers: Erasure Schemes Using Generalized Polar Codes: Zer…
When information is to be transmitted over an unknown, possibly unreliable channel, an erasure option at the decoder is desirable. Using constant-composition random codes, we propose a generalization of Csiszar and Korner's Maximum Mutual…
Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and…
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…
A transform that is universally polarizing over a set of channels with memory is presented. Memory may be present in both the input to the channel and the channel itself. Both the encoder and the decoder are aware of the input distribution,…
Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the corresponding code length is limited to the power of two. In this paper, we establish a…
Recently, a new class of error-control codes, the polar codes, have attracted much attention. The polar codes are the first known class of capacity-achieving codes for many important communication channels. In addition, polar codes have…
This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…
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…
Polar codes are a new class of block codes with an explicit construction that provably achieve the capacity of various communications channels, even with the low-complexity successive-cancellation (SC) decoding algorithm. Yet, the more…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
Polar codes are the first class of channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels with efficient encoding and decoding algorithms. But the weight spectrum of Polar codes is relatively poor…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
This work presents a polar coding scheme for fading channels, focusing primarily on fading binary symmetric and additive exponential noise channels. For fading binary symmetric channels, a hierarchical coding scheme is presented, utilizing…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
It's known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. We call the coupled information bits the correlated bits. In this paper, concatenation schemes are studied for polar codes (as inner…
Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
Using tools developed in a recent work by Shen and the second author, in this paper we carry out an in-depth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding…