8 research outputs found
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
CRC-Aided Belief Propagation List Decoding of Polar Codes
Although iterative decoding of polar codes has recently made huge progress
based on the idea of permuted factor graphs, it still suffers from a
non-negligible performance degradation when compared to state-of-the-art
CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show
that iterative decoding of polar codes based on the belief propagation list
(BPL) algorithm can approach the error-rate performance of CA-SCL decoding and,
thus, can be efficiently used for decoding the standardized 5G polar codes.
Rather than only utilizing the cyclic redundancy check (CRC) as a stopping
condition (i.e., for error-detection), we also aim to benefit from the
error-correction capabilities of the outer CRC code. For this, we develop two
distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv
(BCJR)-based approach and a sum product algorithm (SPA)-based approach.
Further, an optimized selection of permuted factor graphs is analyzed and shown
to reduce the decoding complexity significantly. Finally, we benchmark the
proposed CRC-aided belief propagation list (CA-BPL) to state-of-the-art 5G
polar codes under CA-SCL decoding and, thereby, showcase an error-rate
performance not just close to the CA-SCL but also close to the maximum
likelihood (ML) bound as estimated by ordered statistic decoding (OSD).Comment: Submitted to IEEE for possible publicatio
Successive Cancellation Automorphism List Decoding of Polar Codes
The discovery of suitable automorphisms of polar codes gained a lot of
attention by applying them in Automorphism Ensemble Decoding (AED) to improve
the error-correction performance, especially for short block lengths. This
paper introduces Successive Cancellation Automorphism List (SCAL) decoding of
polar codes as a novel application of automorphisms in advanced Successive
Cancellation List (SCL) decoding. Initialized with L permutations sampled from
the automorphism group, a superposition of different noise realizations and
path splitting takes place inside the decoder. In this way, the SCAL decoder
automatically adapts to the channel conditions and outperforms the
error-correction performance of conventional SCL decoding and AED. For a polar
code of length 128, SCAL performs near Maximum Likelihood (ML) decoding with
L=8, in contrast to M=16 needed decoder cores in AED. Application-Specific
Integrated Circuit (ASIC) implementations in a 12 nm technology show that
high-throughput, pipelined SCAL decoders outperform AED in terms of energy
efficiency and power density, and SCL decoders additionally in area efficiency.Comment: 5 pages, 5 figures, submitted to IEEE for possible publicatio
Concept development of a Mach 4 high-speed civil transport
A study was conducted to configure and analyze a 250 passenger, Mach 4 High Speed Civil Transport with a design range of 6500 n.mi. The design mission assumed an all-supersonic cruise segment and no community noise or sonic boom constraints. The study airplane was developed in order to examine the technology requirements for such a vehicle and to provide an unconstrained baseline from which to assess changes in technology levels, sonic boom limits, or community noise constraints in future studies. The propulsion, structure, and materials technologies utilized in the sizing of the study aircraft were assumed to represent a technology availability date of 2015. The study airplane was a derivative of a previously developed Mach 3 concept and utilized advanced afterburning turbojet engines and passive airframe thermal protection. Details of the configuration development, aerodynamic design, propulsion system, mass properties, and mission performance are presented. The study airplane was estimated to weigh approx. 866,000 lbs. Although an aircraft of this size is a marginally acceptable candidate to fit into the world airport infrastructure, it was concluded that the inclusion of community noise or sonic boom constraints would quickly cause the aircraft to grow beyond acceptable limits using the assumed technology levels
Component Training of Turbo Autoencoders
Isolated training with Gaussian priors (TGP) of the component autoencoders of
turbo-autoencoder architectures enables faster, more consistent training and
better generalization to arbitrary decoding iterations than training based on
deep unfolding. We propose fitting the components via extrinsic information
transfer (EXIT) charts to a desired behavior which enables scaling to larger
message lengths () while retaining competitive performance. To
the best of our knowledge, this is the first autoencoder that performs close to
classical codes in this regime. Although the binary cross-entropy (BCE) loss
function optimizes the bit error rate (BER) of the components, the design via
EXIT charts enables to focus on the block error rate (BLER). In serially
concatenated systems the component-wise TGP approach is well known for inner
components with a fixed outer binary interface, e.g., a learned inner code or
equalizer, with an outer binary error correcting code. In this paper we extend
the component training to structures with an inner and outer autoencoder, where
we propose a new 1-bit quantization strategy for the encoder outputs based on
the underlying communication problem. Finally, we discuss the model complexity
of the learned components during design time (training) and inference and show
that the number of weights in the encoder can be reduced by 99.96 %.Comment: Submitted to ISTC 2023,5 page
A Polar Subcode Approach to Belief Propagation List Decoding
Permutation decoding gained recent interest as it can exploit the symmetries
of a code in a parallel fashion. Moreover, it has been shown that by viewing
permuted polar codes as polar subcodes, the set of usable permutations in
permutation decoding can be increased. We extend this idea to pre-transformed
polar codes, such as cyclic redundancy check (CRC)-aided polar codes, which
previously could not be decoded using permutations due to their lack of
automorphisms. Using belief propagation (BP)-based subdecoders, we showcase a
performance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithm
outperforms the previously best performing iterative CRC-aided belief
propagation list (CA-BPL) decoder both in error-rate performance and decoding
latency.Comment: 6 pages, submitted to IEEE for possible publicatio