Related papers: On the Construction and Decoding of Concatenated P…
Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error…
Recently, Martinez-Penas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted…
Polar codes are a family of capacity-achieving error-correcting codes, and they have been selected as part of the next generation wireless communication standard. Each polar code bit-channel is assigned a reliability value, used to…
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…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
Polar codes are considered the latest major breakthrough in coding theory. Polar codes were introduced by Ar{\i}kan in 2008. In this letter, we show that the binary polar codes are the same as the optimized codes for bitwise multistage…
To decode a short linear block code, ordered statics decoding (OSD) and/or the $A^*$ decoding are usually considered. Either OSD or the $A^*$ decoding utilizes the magnitudes of the received symbols to establish the most reliable and…
Polar codes can theoretically achieve very competitive Frame Error Rates. In practice, their performance may depend on the chosen decoding procedure, as well as other parameters of the communication system they are deployed upon. As a…
A practical rate-matching system for constructing rate-compatible polar codes is proposed. The proposed polar code circular buffer rate-matching is suitable for transmissions on communication channels that support hybrid automatic repeat…
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…
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…
Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments,…
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
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…
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…
In this letter we propose a new hybrid code called "RM-Polar" codes. This new codes are constructed by combining the construction of Reed-Muller (RM) code and Polar code. It has much larger minimum Hamming distance than Polar codes,…
Polar codes are a recent family of error-correcting codes with a number of desirable characteristics. Their disruptive nature is illustrated by their rapid adoption in the $5^{th}$-generation mobile-communication standard, where they are…
Generalized Concatenated codes are a code construction consisting of a number of outer codes whose code symbols are protected by an inner code. As outer codes, we assume the most frequently used Reed-Solomon codes; as inner code, we assume…
Code decompositions (a.k.a code nestings) are used to design good binary polar code kernels. The proposed kernels are in general non-linear and show a better rate of polarization under successive cancelation decoding, than the ones…