Related papers: Enumeration of Minimum Hamming Weight Polar Codewo…
Polar codes are a class of channel capacity achieving codes that has been selected for the next generation of wireless communication standards. Successive-cancellation (SC) is the first proposed decoding algorithm, suffering from mediocre…
Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…
Applications of massive machine-type communications, such as sensor networks, smart metering, 'internet-of-things', or process and factory automation, are forecast to have great economic impact in the next five to ten years. Low-complexity…
Due to their capacity-achieving property, polar codes have become one of the most attractive channel codes. To date, the successive cancellation list (SCL) decoding algorithm is the primary approach that can guarantee outstanding…
We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator ($\cM$), rather than on the weight enumerator ($\cW$)…
Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes…
This paper presents a hardware architecture of fast simplified successive cancellation (fast-SSC) algorithm for polar codes, which significantly reduces the decoding latency and dramatically increases the throughput. Algorithmically,…
We propose a novel coupling technique for the design of polar codes of length N, making them decodable through a sliding window of size M < N. This feature allows to reduce the computational complexity of the decoder, an important…
The performance of short polar codes under successive cancellation (SC) and SC list (SCL) decoding is analyzed for the case where the decoder messages are coarsely quantized. This setting is of particular interest for applications requiring…
We show that successive cancellation list decoding can be formulated exclusively using log-likelihood ratios. In addition to numerical stability, the log-likelihood ratio based formulation has useful properties which simplify the sorting…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
This work presents a fast successive-cancellation list flip (Fast-SCLF) decoding algorithm for polar codes that addresses the high latency issue associated with the successive-cancellation list flip (SCLF) decoding algorithm. We first…
Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction. This work aims to increase the throughput of polar decoder hardware by an order of magnitude relative to the state of the art…
Product codes are widely used in data-storage, optical and wireless applications. Their analytical performance evaluation usually relies on the truncated union bound, which provides a low error rate approximation based on the minimum…
A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC)…
We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…
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…
We present a method of constructing rate-compatible polar codes that are capacity-achieving with low-complexity sequential decoders. The proposed code construction allows for incremental retransmissions at different rates in order to adapt…
In this letter, we introduce an efficient method for estimating weight distributions of polar codes and polarization-adjusted convolutional (PAC) codes. Based on a recursive algorithm of computing the weight enumerating functions of polar…
We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…