Related papers: Polar codes for q-ary channels, q=2^r

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…

Polar codes are the first proven capacity-achieving codes. Recently, they are adopted as the channel coding scheme for 5G due to their superior performance.A polar code for encoding length-K information bits in length-N codeword could be…

Classically, no information can be transmitted through a depolarising, that is a completely noisy, channel. We show that by combining a depolarising channel with another channel in an indefinite causal order---that is, when there is…

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…

In this paper, we consider the problem of polar coding for block fading channels, with emphasis on those with instantaneous channel state information (CSI) at neither the transmitter nor the receiver. Our approach is to decompose a block…

We consider classical-quantum (cq-)channels with memory, and establish that Ar{\i}kan-constructed polar codes achieve the classical capacity for two key noise models, namely for (i) qubit erasures and (ii) unital qubit noise with channel…

Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying the two recently developed…

This study proposes \emph{modular arithmetic erasure channels} (MAECs), a novel class of erasure-like channels with an input alphabet that need not be binary. This class contains the binary erasure channel (BEC) and some other known…

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…

We consider the problem of using polar codes over slow fading wireless channels. For design, we focus on a parallel slow fading channel with 2 blocks, and polar codes with rate <= 1/2. Motivated by Arikan's systematic polar code…

Polar code visibly approaches channel capacity in practice and is thereby a constituent code of the 5G standard. Compared to low-density parity-check code, however, the performance of short-length polar code has rooms for improvement that…

A reduced complexity algorithm is presented for computing the log-likelihood ratios arising in the successive cancellation decoder for polar codes with large kernels of arbitrary dimension. The proposed algorithm exploits recursive trellis…

We prove that for any additive noise channel over $\mathbb{F}_q$, there exist error-correcting codes approaching channel capacity encodable by arithmetic circuits (with weighted addition gates) over $\mathbb{F}_q$ of size $O(n)$ and depth…

A major challenge in quantum communication is addressing the negative effects of noise on channel capacity, especially for completely depolarizing channels, where information transmission is inherently impossible. The concept of indefinite…

We consider binary input deletion/substitution channels, which model certain types of synchronization errors encountered in practice. Specifically, we focus on the regime of small deletion and substitution probabilities, and by extending an…

ABS polar codes were recently proposed to speed up polarization by swapping certain pairs of adjacent bits after each layer of polar transform. In this paper, we observe that applying the Arikan transform $(U_i, U_{i+1}) \mapsto…

Fast polarization is an important and useful property of polar codes. It was proved for the binary polarizing $2 \times 2$ kernel by Arikan and Telatar. The proof was later generalized by Sasoglu. We give a simplified proof.

We study the error detection problem in $ q $-ary asymmetric channels wherein every input symbol $ x_i $ is mapped to an output symbol $ y_i $ satisfying $ y_i \geq x_i $. A general setting is assumed where the noise vectors are…

We describe some pseudorandom properties of binary linear codes achieving capacity on the binary erasure channel under bit-MAP decoding (as shown in Kudekar et al this includes doubly transitive codes and, in particular, Reed-Muller codes).…

Polar codes is promising because they can provably achieve the channel capacity while having an explicit construction method. Lots of work have been done for the bit-based decoding algorithm for polar codes. In this paper, generalized…