In the Shannon lecture at 2019 International Symposium on Information Theory (ISIT), Arıkan proposed to employ a one-to-one convolutional transform as pre-coding step before polar transform. The resulting codes of this concatenation are called polarization-adjusted (PAC) codes. scheme, pair mapper and demapper preand postprocessing devices deployed around memoryless channel, which provides polarized information an outer decoder leading improved error correction performance code. paper, list...

Channel coding plays a pivotal role in ensuring reliable communication over wireless channels. With the growing need for ultra-reliable emerging use cases, significance of channel has amplified. Furthermore, minimizing decoding latency is crucial critical-mission applications, while optimizing energy efficiency paramount mobile and Internet Things (IoT) communications. As fifth generation (5G) communications currently operation 5G-advanced on horizon, objective this paper to assess prominent...

CRC-Polar codes under SC list decoding are well-regarded for their competitive error performance. This paper examines these by focusing on minimum weight codewords and breaking them down into the rows of polar transform. Inspired significant impact parity check bits positions, we apply a shifted rate-profile polarization-adjusted convolutional (PS-PAC) codes, thereby achieving similar improvements in distribution through precoding. The results demonstrate improvement performance, up to 0.5...

Minimum weight codewords play a crucial role in the error correction performance of linear block code. In this work, we establish an explicit construction for these polar codes as sum generator matrix rows, which can then be used foundation two applications. first application, obtain lower bound number minimum-weight (a.k.a. coefficient), matches exact established previously literature. second derive novel method that modifies information set rate profile) and PAC order to reduce...

In successive cancellation list (SCL) decoding, the pruning operation retains L paths with highest likelihoods. However, correct path might be among low likelihoods due to channel noise. this case, is eliminated from list. work, we study event of elimination and analyze where how occurs. A modified scheme named shifted-pruning over a set low-reliability bit-channels critical bits proposed aiming avoid in additional decoding attempts after failure Shifted-pruning realized by selecting k + 1...

Polarization-adjusted convolutional (PAC) codes are special concatenated in which we employ a one-to-one transform as pre-coding step before the polar transform. In this scheme, (as mapper) and successive cancellation process demapper) present synthetic vector channel to transformation. The numerical results show that concatenation improves Hamming distance properties of codes. Motivated by fact parallel list Viterbi algorithm (LVA) sorts candidate paths locally at each trellis node, work,...

The minimum Hamming distance of a linear block code is the smallest number bit changes required to transform one valid codeword into another. code's determines error-correcting capabilities. Furthermore, weight codewords, a.k.a. error coefficient, gives good comparative measure for rate (BLER) codes with identical distance, in particular at high SNR regime under maximum likelihood (ML) decoding. A smaller coefficient would give lower BLER. Unlike polar codes, closed-form expression...

In the successive cancellation list (SCL) decoding of polar codes, as size increases, error correction performance improves. However, a large results in high computational complexity and memory requirement.In this paper, we investigate process by introducing new parameter named path metric range (PMR) to elucidate properties evolution metrics (PMs) within throughout process. Then, advocate that can change stepwise depending on PMR. As result, propose stepped scheme which conventional is...

In polarization-adjusted convolutional (PAC) codes, a transform is employed as precoding stage before the polar transform. It turned out that improves weight distribution of codes according. That could be main reason for superiority error correction performance PAC relative to codes. this work, we explicitly show why reduces number minimum-weight codewords. Furthermore, where not effective in improvement distribution. Eventually, evaluate FER gain obtainable from reducing min-weight...

The weight distribution of an error correction code is a critical determinant its error-correcting performance. In the case polar codes, minimum w <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> (equal to distance <italic xmlns:xlink="http://www.w3.org/1999/xlink">d</i> ) only for which explicit enumerator formula currently available. Having closed-form enumerators codewords with weights greater than not simplifies enumeration process...

Polar codes are constructed based on the reliability of bit-channels. This construction suits successive cancellation (SC) decoding, where one error in estimation bits fails decoding. However, SC list (SCL) correct path may remain by tolerating multiple penalties. characteristic decoding demands a different approach code construction. In this work, we modify conventional greedy search algorithm which bit-swapping is employed to re-distribute low-reliability subblocks aiming for reduction...

Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, size search space and consequently complexity grows exponentially, making it impractical employed for long In this paper, we propose an approach constrain patterns under a recently introduced near ML scheme called guessing random additive noise (GRAND). approach, syndrome-based constraints which divide into disjoint sets are progressively evaluated. By employing p extracted from...

In successive cancellation list (SCL) decoding, the tree pruning operation retains L best paths with respect to a metric at every decoding step. However, correct path might be among worst due imposed penalties. this case, is pruned and process fails. Shifted-pruning (SP) scheme can recover by additional attempts when fails, in which window shifted over bits high likelihood of elimination path, one time. work, we generalize more freedom shifting window, aiming improve error correction...

The number of minimum weight codewords, a.k.a error coefficient, is a good comparative measure for the block rate (BLER) linear code, in particular high SNR regime. smaller lower BLER. Unlike polar codes, coefficient polarization-adjusted convolutional (PAC) codes cannot be determined easily due to precoding stage. In this work, we propose an enumeration method that considers impact on codewords codes. This relative simplifies process significantly compared with conventional methods as...

The weight distribution of error correction codes is a critical determinant their error-correcting performance, making enumeration utmost importance. In the case polar codes, minimum $\wm$ (which equal to distance $d$) only for which an explicit enumerator formula currently available. Having closed-form enumerators codewords with weights greater than not simplifies process but also provides valuable insights towards constructing better polar-like codes. this paper, we contribute...

Polar codes are normally constructed based on the reliability of sub-channels in polarized vector channel. Code construction is compatible with successive cancellation decoding. However, due to poor Hamming distance properties, designed cannot perform well near maximum likelihood decoders. In this work, we propose a new approach that modifies polar and PAC significantly lower number codewords minimum (a.k.a. error coefficient). This recognition all rows transform involved formation...

Error correction performance of finite‐length polar codes has been a major concern in the past decade. This Letter presents method for improving error cyclic redundancy check (CRC)‐aided successive cancellation list decoding medium block‐lengths with high code rates. In proposed scheme, one‐time repetition least reliable bit‐channels along partial protection message is employed to correct error(s) when fails. The results show an improvement nearly 0.2 dB performance.

The recently introduced maximum-likelihood (ML) decoding scheme called guessing random additive noise (GRAND) has demonstrated a remarkably low time complexity in high signal-to-noise ratio (SNR) regimes. However, the is not as at SNR regimes and code rates. To mitigate this concern, we propose for near-ML variant of GRAND ordered reliability bits (or ORBGRAND), which divides codewords into segments based on properties underlying code, generates sub-patterns each segment consistent with...

&lt;div&gt;Polarization-adjusted convolutional (PAC) codes are special concatenated in which we employ a one-to-one transform as pre-coding step before the polar transform. In this scheme, (as mapper) and successive cancellation process demapper) present synthetic vector channel to transformation. The numerical results show that concatenation improves Hamming distance properties of codes. &lt;/div&gt;&lt;div&gt;In work, implement parallel list Viterbi algorithm (LVA) how error correction...

In the Shannon lecture at 2019 International Symposium on Information Theory (ISIT), Arıkan proposed to employ a one-to-one convolutional transform as pre-coding step before polar transform. The resulting codes of this concatenation are called polarization-adjusted (PAC) codes. scheme, pair mapper and demapper pre- postprocessing devices deployed around memoryless channel, which provides polarized information an outer decoder leading improved error correction performance code. paper, list...

Rate matching techniques, such as puncturing and shortening, have been developed for polar codes to accommodate the specific code length requirements in practical applications. However, existing shortening techniques cannot be directly applied polarization-adjusted convolutional (PAC) codes. In this work, we propose an approach shorten PAC by imposing constraints on precoding process based patterns. The proposed technique leads up 0.2 dB power gain error correction performance compared...