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Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…
Polar codes are of great interest since they are the first provably capacity-achieving forward error correction codes. To improve throughput and to reduce decoding latency of polar decoders, maximum likelihood (ML) decoding units are used…
Polar encoding, described by Arikan in IEEE Transactions on Information Theory, Vol. 55, No. 7, July 2009, was a milestone for telecommunications. A Polar code distributes information among high and low-capacity channels, showing the…
We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation and an Ar{\i}kan-style transformation is applied using this operation. It is shown that as…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
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…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
We consider non-binary polarization transform problem of polar codes. The focus of this work is on finding equidistant (or almost equidistant) polarizing transforms to maximize the minimum distance and to approach the equidistant distant…
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…
When a neural network (NN) is used to decode a polar code, its training complexity scales exponentially as the code block size (or to be precise, as a number of message bits) increases. Therefore, existing solutions that use a neural…
The KV cache in large language models is a dominant factor in memory usage, limiting their broader applicability. Quantizing the cache to lower bit widths is an effective way to reduce computational costs; however, previous methods struggle…
Polar codes have gained significant amount of attention during the past few years and have been selected as a coding scheme for the next generation of mobile broadband standard. Among decoding schemes, successive-cancellation list (SCL)…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
For the polar codes introduced by Arikan in 2009, the first code family achieving the capacity of binary-input discrete memoryless channels (BIDMCs) with low-complexity encoding and decoding, it is crucial to evaluate the reliability of the…
The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
In this paper, we propose a method to obtain the optimal metric function at each depth of the polarization tree through a process we call polarization of the metric function. This polarization process generates an optimal metric at…
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 this paper, we establish the partial order (POs) for both the binary erasure channel (BEC) and the binary memoryless symmetric channel (BMSC) under any block rate-matched polar codes. Firstly, we define the POs in the sense of…
Good quantum error-correcting codes that fulfill practical considerations, such as simple encoding circuits and efficient decoders, are essential for functional quantum information processing systems. Quantum polar codes satisfy some of…