Related papers: On Distance Properties of Convolutional Polar Code…
The polarization process of polar codes over a ternary alphabet is studied. Recently it has been shown that the scaling of the blocklength of polar codes with prime alphabet size scales polynomially with respect to the inverse of the gap…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
Polar codes have received growing attention in the past decade and have been selected as the coding scheme for the control channel in the fifth generation (5G) wireless communication systems. However, the conventional polar codes have only…
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…
Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this…
The definition of polar codes given by Arikan is explicit, but the construction complexity is an issue. This is due to the exponential growth in the size of the output alphabet of the bit-channels as the codeword length increases. Tal and…
A new score function is proposed for stack decoding of polar codes, which enables one to accurately compare paths of different lengths. The proposed score function includes bias, which reflects the average behaviour of the correct path.…
The long-haul communication systems can offer ultra high-speed data transfer rates but suffer from burst errors. The high-rate and high-performance staircase codes provide an efficient way for long-haul transmission. The staircase coding…
ABS polar codes were recently proposed to speed up polarization by swapping certain pairs of adjacent bits after each layer of polar transform. In this paper, we observe that applying the Arikan transform $(U_i, U_{i+1}) \mapsto…
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…
Consider the problem of constructing a polar code of block length $N$ for the transmission over a given channel $W$. Typically this requires to compute the reliability of all the $N$ synthetic channels and then to include those that are…
The discovery of suitable automorphisms of polar codes gained a lot of attention by applying them in Automorphism Ensemble Decoding (AED) to improve the error-correction performance, especially for short block lengths. This paper introduces…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
We consider polar subcodes (PSCs), which are polar codes (PCs) with dynamically-frozen symbols, to increase the minimum distance as compared to corresponding PCs. A randomized nested PSC construction with a low-rate PSC and a high-rate PC,…
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…
Polar codes, discovered by Ar{\i}kan, are the first error-correcting codes with an explicit construction to provably achieve channel capacity, asymptotically. However, their error-correction performance at finite lengths tends to be lower…
We propose a novel coupling technique for the design of polar codes of length N, making them decodable through a sliding window of size M < N. This feature allows to reduce the computational complexity of the decoder, an important…
Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new…
We present a rate-compatible polar coding scheme that achieves the capacity of any family of channels. Our solution generalizes the previous results [1], [2] that provide capacity-achieving rate-compatible polar codes for a degraded family…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…