相关论文: Density Devolution for Ordering Synthetic Channels

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 codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of…

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…

In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…

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…

We consider the problem of determining the trade-off between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters…

This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter $p$ (BDC$_p$) every bit is deleted…

A pruned variant of polar coding is proposed for binary erasure channels. For sufficiently small $\varepsilon>0$, we construct a series of capacity achieving codes with block length $N=\varepsilon^{-5}$, code rate…

In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets…

This paper introduces a neural polar decoder (NPD) for deletion channels with a constant deletion rate. Existing polar decoders for deletion channels exhibit high computational complexity of $O(N^4)$, where $N$ is the block length. This…

We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…

This paper focuses on low complexity successive cancellation list (SCL) decoding of polar codes. In particular, using the fact that splitting may be unnecessary when the reliability of decoding the unfrozen bit is sufficiently high, a novel…

While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit-channels, finding optimal polar codes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL) decoding in…

Polar codes have received growing attention in the past decade and have been selected as the coding scheme for the control channel in the fifth generation (5G) wireless communication systems. However, the conventional polar codes have only…

Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input…

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…

This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…

We consider lossy source compression of a binary symmetric source using polar codes and the low-complexity successive encoding algorithm. It was recently shown by Arikan that polar codes achieve the capacity of arbitrary symmetric…

The strange attractor represents a complex pattern of behavior in dynamic systems. This paper introduces a strange attractor for synthetic channels in polar coding as a result of a geometric property of density evolution that is a polar…

We survey the known list decoding algorithms for polar codes and compare their complexity. Index terms: Polar codes; Reed-Muller codes; successive cancellation decoding.