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Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM…
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…
In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made…
For finite length polar codes, channel polarization leaves a significant number of channels not fully polarized. Adding a Cyclic Redundancy Check (CRC) to better protect information on the semi-polarized channels has already been…
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…
Long polar codes can achieve the capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancelation (SC) decoding algorithm. But for polar codes with short and moderate code length, the decoding…
We survey the known list decoding algorithms for polar codes and compare their complexity. Index terms: Polar codes; Reed-Muller codes; successive cancellation decoding.
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…
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…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Recently, automorphism ensemble decoding (AED) has drawn research interest as a more computationally efficient alternative to successive cancellation list (SCL) decoding of polar codes. Although AED has demonstrated superior performance for…
Tailoring polar code construction for decoding algorithms beyond successive cancellation has remained a topic of significant interest in the field. However, despite the inherent nested structure of polar codes, the use of sequence models in…
$2^m$-ary modulation creates $m$ bit channels which are neither independent nor identical, and this causes problems when applying polar coding because polar codes are designed for independent identical channels. Different from the existing…
In practical communication systems, knowledge of channel models is often absent, and consequently, transceivers need be designed based on empirical data. In this work, we study data-driven approaches to reliably choosing decoding metrics…
We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
For finite coupling lengths, terminated spatially coupled low-density parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in conjunction…
Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the analysis and construction of polar codes involve the complex iterative-calculation. In…
The so-called fast polar decoding schedules are meant to improve the decoding speed of the sequential-natured successive cancellation list decoders. The decoding speedup is achieved by replacing various parts of the serial decoding process…
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…