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In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite…
Successive cancellation list (SCL) decoders of polar codes excel in practical performance but pose challenges for theoretical analysis. Existing works either limit their scope to erasure channels or address general channels without taking…
This paper focuses on the recently introduced Successive Cancellation Flip (SCFlip) decoder of polar codes. Our contribution is twofold. First, we propose the use of an optimized metric to determine the flipping positions within the SCFlip…
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…
For polar codes with short-to-medium code length, list successive cancellation decoding is used to achieve a good error-correcting performance. However, list pruning in the current list decoding is based on the sorting strategy and its…
While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit-channels, finding optimal polar codes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL) decoding in…
In this paper, we consider the problem of polar coding for block fading channels, with emphasis on those with instantaneous channel state information (CSI) at neither the transmitter nor the receiver. Our approach is to decompose a block…
Dynamic successive cancellation flip (DSCF) decoding of polar codes is a powerful algorithm that can achieve the error correction performance of successive cancellation list (SCL) decoding, with a complexity that is close to that of…
Bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLC) are commonly used to combine polar codes with high order modulation. While BICM benefits from simple design and the separation of coding and modulation, MLC shows…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
Polar codes have received increasing attention in the past decade, and have been selected for the next generation of wireless communication standard. Most research on polar codes has focused on codes constructed from a $2\times2$…
This paper introduces algorithms for the successive-cancellation decoding and the successive-cancellation list decoding of binary polar source/channel codes. By using the symmetric parametrization of conditional probability, we reduce both…
Polar codes, introduced recently by Ar\i kan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation,…
We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error…
In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. The proposed multi-kernel polar…
For polar codes, successive cancellation list (SCL) decoding algorithm significantly improves finite-length performance compared to SC decoding. SCL-flip decoding can further enhance the performance but the gain diminishes as code length…
We consider the compound capacity of polar codes under successive cancellation decoding for a collection of binary-input memoryless output-symmetric channels. By deriving a sequence of upper and lower bounds, we show that in general the…
In this paper, we design and compare multilevel polar coding (MLPC) and bit-interleaved polar coded modulation (BIPCM) for uplink sparse code multiple access (SCMA) systems that operate over fast and block fading channels. Both successive…
We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered…
Typically, forward error correction (FEC) codes are designed based on the minimization of the error rate for a given code rate. However, for applications that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive…