1,929 research outputs found
Design, Performance, and Complexity of CRC-Aided List Decoding of Convolutional and Polar Codes for Short Messages
Motivated by the need to communicate short control messages in 5G and beyond,
this paper carefully designs codes for cyclic redundancy check (CRC)-aided list
decoding of tail-biting convolutional codes (TBCCs) and polar codes. Both codes
send a 32-bit message using an 11-bit CRC and 512 transmitted bits. We aim to
provide a careful, fair comparison of the error performance and decoding
complexity of polar and TBCC techniques for a specific case. Specifically, a
TBCC is designed to match the rate of a (512, 43) polar code, and optimal
11-bit CRCs for both codes are designed. The paper examines the distance
spectra of the polar and TBCC codes, illuminating the different distance
structures for the two code types. We consider both adaptive and non-adaptive
CRC-aided list decoding schemes. For polar codes, an adaptive decoder must
start with a larger list size to avoid an error floor. For rate-32/512 codes
with an 11-bit CRC, the optimized CRC-TBCC design achieves a lower total
failure rate than the optimized CRC-polar design. Simulations showed that the
optimized CRC-TBCC design achieved significantly higher throughput than the
optimized CRC-polar design, so that the TBCC solution achieved a lower total
failure rate while requiring less computational complexity.Comment: First revision submitted to IEEE Transactions on Communication
Rate-Compatible Polar Codes for Automorphism Ensemble Decoding
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 specific code parameters, a flexible code design that can
accommodate varying code rates does not yet exist. This work proposes a
theoretical framework for constructing rate-compatible polar codes with a
prescribed automorphism group, which is a key requirement for AED. We first
prove that a one-bit granular sequence with useful automorphisms cannot exist.
However, by allowing larger steps in the code dimension, flexible code
sequences can be constructed. An explicit synthetic channel ranking based on
the -expansion is then proposed to ensure that all constructed codes
possess the desired symmetries. Simulation results, covering a broad range of
code dimensions and blocklengths, show a performance comparable to that of 5G
polar codes under cyclic redundancy check (CRC)-aided SCL decoding, however,
with lower complexity.Comment: 5 pages, 2 figures, submitted to IEEE for possible publicatio
Partitioned List Decoding of Polar Codes: Analysis and Improvement of Finite Length Performance
Polar codes represent one of the major recent breakthroughs in coding theory
and, because of their attractive features, they have been selected for the
incoming 5G standard. As such, a lot of attention has been devoted to the
development of decoding algorithms with good error performance and efficient
hardware implementation. One of the leading candidates in this regard is
represented by successive-cancellation list (SCL) decoding. However, its
hardware implementation requires a large amount of memory. Recently, a
partitioned SCL (PSCL) decoder has been proposed to significantly reduce the
memory consumption. In this paper, we examine the paradigm of PSCL decoding
from both theoretical and practical standpoints: (i) by changing the
construction of the code, we are able to improve the performance at no
additional computational, latency or memory cost, (ii) we present an optimal
scheme to allocate cyclic redundancy checks (CRCs), and (iii) we provide an
upper bound on the list size that allows MAP performance.Comment: 2017 IEEE Global Communications Conference (GLOBECOM
Low-Complexity Puncturing and Shortening of Polar Codes
In this work, we address the low-complexity construction of shortened and
punctured polar codes from a unified view. While several independent puncturing
and shortening designs were attempted in the literature, our goal is a unique,
low-complexity construction encompassing both techniques in order to achieve
any code length and rate. We observe that our solution significantly reduces
the construction complexity as compared to state-of-the-art solutions while
providing a block error rate performance comparable to constructions that are
highly optimized for specific lengths and rates. This makes the constructed
polar codes highly suitable for practical application in future communication
systems requiring a large set of polar codes with different lengths and rates.Comment: to appear in WCNC 2017 - "Polar Coding in Wireless Communications:
Theory and Implementation" Worksho
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