arXiv subjects

Ruslan Morozov

Publications and source records attributed to Ruslan Morozov.

6 recordsLinked to original sources

arXiv2025

Simple Finite-Length Achievability and Converse Bounds for the Deletion Channel and the Insertion Channel

We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse bound, which, though available for any channel, is inefficient and not easily computable without a good reference distribution over the output alphabet. We obtain a reference output distribution for a general finite-input finite-output channel and provide a simple formula for the converse bound on the capacity employing this distribution. We then evaluate the bound for the deletion channel with a finite block length, and show that the resulting upper bound on the code size is tighter than that for a binary erasure channel, which is the only alternative converse bound for the finite-length setting. We also provide similar results for the insertion channel. Furthermore, we present a simple algorithm for computing an achievability bound for a general discrete-input discrete-output channel. Although the algorithm has exponential complexity, it is useful for comparison purposes.

cs.IT↗

arXiv2024

Channels with Markov Synchronization Errors: Information Stability and Capacity Bounds

Particularly motivated by DNA storage channels, we consider channels with synchronization errors modeled as insertions and deletions, along with substitutions. We focus on the case where the synchronization error process has memory and investigate the information stability of these channels, hence the existence of their Shannon capacity. We assume that the synchronization errors are governed by a stationary and ergodic finite state Markov chain and prove that such a channel is information-stable, which implies the existence of a coding scheme that achieves the limit of mutual information. This result implies the existence of the Shannon capacity for a wide range of channels with synchronization errors, with different applications, including DNA storage. We also provide specific examples of deletion channels with Markov memory and numerically evaluate their capacity bounds, thereby allowing us to quantify the capacity difference between memoryless deletion channels and those with memory with the same deletion probability and reveal that having memory increases the channel capacity.

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arXiv2020

Convolutional Polar Kernels

A family of polarizing kernels is presented together with polynomial-complexity algorithm for computing scaling exponent. The proposed convolutional polar kernels are based on convolutional polar codes, also known as b-MERA codes. For these kernels, a polynomial-complexity algorithm is proposed to find weight spectrum of unrecoverable erasure patterns, needed for computing scaling exponent. As a result, we obtain scaling exponent and polarization rate for convolutional polar kernels of size up to 1024.

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arXiv2020

Efficient List Decoding of Convolutional Polar Codes

An efficient implementation of min-sum SC/list decoding of convolutional polar codes is proposed. The complexity of the proposed implementation of SC decoding is more than two times smaller than the straightforward implementation. Moreover, the proposed list decoding algorithm does not require to copy any LLRs during decoding.

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arXiv2019

On Distance Properties of Convolutional Polar Codes

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 convolutional polar subcodes is proposed, which provides improved performance under successive cancellation list decoding. For sufficiently large list size, the decoding complexity of convolutional polar subcodes appears to be lower compared to Arikan polar subcodes with the same performance. The error probability of successive cancellation list decoding of convolutional polar subcodes is lower than that of Arikan polar subcodes with the same list size.

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arXiv2018

Fast Sequential Decoding of Polar Codes

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. This enables significant complexity reduction with respect to the original stack algorithm at the expense of a negligible performance loss.

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