Related papers: Universal polar coding and sparse recovery
In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
In this work, we present a deterministic algorithm for computing the entire weight distribution of polar codes. As the first step, we derive an efficient recursive procedure to compute the weight distribution that arises in successive…
Successive cancellation list (SCL) decoding enables polar codes and their generalizations to deliver satisfactory performance in finite-length scenarios but it comes with high latency and complexity. To reduce latency, a partitioned SCL…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
Polar codes are a new family of error correction codes for which efficient hardware architectures have to be defined for the encoder and the decoder. Polar codes are decoded using the successive cancellation decoding algorithm that includes…
Blind recognition of polar codes remains challenging in non-cooperative scenarios, particularly for information-set recognition with known code length. Existing methods mainly rely on threshold decisions determined by the generator-matrix…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
One-bit compressed sensing (1bCS) addresses the recovery of sparse signals from highly quantized measurements, retaining only the sign of each linear measurement. In the support recovery setting, the goal is to identify $\text{supp}(x)$,…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
A successive cancellation list (SCL) decoder with limited list size for polar codes can not be analyzed as a successive cancellation (SC) decoder, nor as a maximum likelihood (ML) decoder, due to the complicated decoding errors caused by…
This paper proposes a method to optimize communication code rates via the application of neural polar decoders (NPDs). Employing this approach enables simultaneous optimization of code rates over input distributions while providing a…
In this paper, we derive the exact weight distributions that emerge during each stage of successive cancellation decoding of polar codes. Though we do not compute the distance spectrum of polar codes, the results allow us to get an estimate…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
Polar codes are the latest breakthrough in coding theory, as they are the first family of codes with explicit construction that provably achieve the symmetric capacity of discrete memoryless channels. Ar{\i}kan's polar encoder and…
A lower bound on minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of generalized cosets of the codes generated by bottom rows of the polarizing matrix. Moreover, a construction of…
Constructing a polar code is all about selecting a subset of rows from a Kronecker power of $[^1_1{}^0_1]$. It is known that, under successive cancellation decoder, some rows are Pareto-better than the other. For instance, whenever a user…
Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been…
The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input…
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…