Related papers: Long Polar vs. LDPC Codes under Complexity-Constra…
The recently-discovered polar codes are widely seen as a major breakthrough in coding theory. These codes achieve the capacity of many important channels under successive cancellation decoding. Motivated by the rapid progress in the theory…
In the conventional successive cancellation (SC) decoder for polar codes, all the future bits to be estimated later are treated as random variables. However, polar codes inevitably involve frozen bits, and their concatenated coding schemes…
We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error…
Monotone chain polar codes generalize classical polar codes to multivariate settings, offering a flexible approach for achieving the entire admissible rate region in the distributed lossless coding problem. However, this flexibility also…
Linear Programming (LP) decoding is emerging as an attractive alternative to decode Low-Density Parity-Check (LDPC) codes. However, the earliest LP decoders proposed for binary and nonbinary LDPC codes are not suitable for use at moderate…
This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints. In particular, when the number of processing elements $P$ that can perform SSC…
Polar codes are the first provable capacity-achieving forward error correction (FEC) codes. In general polar codes can be decoded via either successive cancellation (SC) or belief propagation (BP) decoding algorithm. However, to date…
This paper basically expresses the core fundamentals and brief overview of the research of R. G. GALLAGER [1] on Low-Density Parity-Check (LDPC) codes and various parameters related to LDPC codes like, encoding and decoding of LDPC codes,…
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…
We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a…
Polar codes have become one of the most favorable capacity achieving error correction codes (ECC) along with their simple encoding method. However, among the very few prior successive cancellation (SC) polar decoder designs, the required…
The peeling decoding for spatially coupled low-density parity-check (SC-LDPC) codes is analyzed for a binary erasure channel. An analytical calculation of the mean evolution of degree-one check nodes of protograph-based SC-LDPC codes is…
Motivated by the significant performance gains which polar codes experience under successive cancellation list decoding, their scaling exponent is studied as a function of the list size. In particular, the error probability is fixed and the…
Polar codes has been selected as the channel coding scheme for 5G new radio (NR) control channel. Specifically, a special type of parity-check polar (PC-Polar) codes was adopted in uplink control information (UCI). In this paper, we propose…
This work presents a high throughput and energy efficient multicore (MC) successive cancellation (SC) decoder architecture for polar codes. SC is a low-complexity decoding algorithm with a set of sequential operations. The sequential…
Polar codes are a class of capacity-achieving codes for the binary-input discrete memoryless channels (B-DMCs). However, when applied in channels with intersymbol interference (ISI), the codes may perform poorly with BCJR equalization and…
Successive cancellation list (SCL) decoders of polar codes excel in practical performance but pose challenges for theoretical analysis. Existing works either limit their scope to erasure channels or address general channels without taking…
Multi-kernel polar codes have recently been proposed to construct polar codes of lengths different from powers of two. Decoder implementations for multi-kernel polar codes need to account for this feature, that becomes critical in memory…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
Benefiting from performance advantages under short code lengths, polar codes are well-suited for certain scenarios, such as the future Internet of Things (IoT) applications that require high reliability and low power. Existing list flip…