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Polar codes, introduced by Arikan, achieve the capacity of arbitrary binary-input discrete memoryless channel $W$ under successive cancellation decoding. Any such channel having capacity $I(W)$ and for any coding scheme allowing…
The prevailing opinion in industry and academia is that polar codes are competitive for short code lengths, but can no longer keep up with low-density parity-check (LDPC) codes as block length increases. This view is typically based on the…
Polar codes are newly discovered capacity-achieving codes, which have attracted lots of research efforts. Polar codes can be efficiently decoded by the low-complexity successive cancelation (SC) algorithm and the SC list (SCL) decoding…
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…
Arikan's Polar codes attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper…
Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is…
This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless…
Trellises are crucial graphical representations of codes. While conventional trellises are well understood, the general theory of (tail-biting) trellises is still under development. Iterative decoding concretely motivates such theory. In…
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…
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…
This paper focuses on an improved Gaussian approximation (GA) based construction of polar codes with successive cancellation (SC) decoding over an additive white Gaussian noise (AWGN) channel. Arikan has proven that polar codes with…
Standard decoding approaches for convolutional codes, such as the Viterbi and BCJR algorithms, entail significant complexity when correcting synchronization errors. The situation worsens when multiple received sequences should be jointly…
Quantum reading provides a general framework where to formulate the statistical discrimination of quantum channels. Several paths have been taken for such a problem. However, there is much to be done in the avenue of optimizing channel…
This paper presents an efficient hardware design approach for list successive cancellation (LSC) decoding of polar codes. By applying path-overlapping scheme, the l instances of (l > 1) successive cancellation (SC) decoder for LSC with list…
Belief propagation (BP) is an iterative decoding algorithm for polar codes which can be parallelized effectively to achieve higher throughput. However, because of the presence of error floor due to cycles and stopping sets in the factor…
As a new joint source-channel coding scheme, the double polar (D-Polar) codes have been proposed recently. In this letter, a novel joint source-channel decoder, namely the joint successive cancellation list (J-SCL) decoder, is proposed to…
We show that polar codes can be used to achieve the rate-distortion functions in the problem of hierarchical source coding also known as the successive refinement problem. We also analyze the distributed version of this problem,…
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…
Polar codes have been gaining a lot of interest due to it being the first coding scheme to provably achieve the symmetric capacity of a binary memoryless channel with an explicit construction. However, the main drawback of polar codes is…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…