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This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…
We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a joint successive cancellation decoder is deployed at the…
Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error…
A polar-coded transmission (PCT) scheme with joint channel estimation and decoding is proposed for channels with unknown channel state information (CSI). The CSI is estimated via successive cancellation (SC) decoding and the constraints…
Polar codes were recently introduced by Ar\i kan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code…
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…
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…
Consider the problem of constructing a polar code of block length $N$ for the transmission over a given channel $W$. Typically this requires to compute the reliability of all the $N$ synthetic channels and then to include those that are…
A heuristic construction of polar codes for successive cancellation list (SCL) decoding with a given list size is proposed to balance the trade-off between performance measured in frame error rate (FER) and decoding complexity. Furthermore,…
Polar codes are of great interests because they provably achieve the capacity of both discrete and continuous memoryless channels while having an explicit construction. Most existing decoding algorithms of polar codes are based on bit-wise…
Improved bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is…
Targeting high-throughput and low-power communications, we implement two successive cancellation (SC) decoders for polar codes. With $16nm$ ASIC technology, the area efficiency and energy efficiency are $4Tbps/mm^2$ and $0.63pJ/bit$,…
In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density…
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…
Achieving information-theoretic security using explicit coding scheme in which unlimited computational power for eavesdropper is assumed, is one of the main topics is security consideration. It is shown that polar codes are capacity…
A deep-learning-aided successive-cancellation list (DL-SCL) decoding algorithm for polar codes is introduced with deep-learning-aided successive-cancellation (DL-SC) decoding being a specific case of it. The DL-SCL decoder works by allowing…
Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications.…
In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
This paper presents non-binary polar codes for the two-user multiple-access channel (MAC). The bit error rate (BER) performances of the non-binary polar codes with different kernel factors have been investigated in detail to select a proper…