1,879 research outputs found
Mitigating Clipping Effects on Error Floors under Belief Propagation Decoding of Polar Codes
In this work, we show that polar belief propagation (BP) decoding exhibits an
error floor behavior which is caused by clipping of the log-likelihood ratios
(LLR). The error floor becomes more pronounced for clipping to smaller
LLR-values. We introduce a single-value measure quantifying a "relative error
floor", showing, by exhaustive simulations for different lengths, that the
error floor is mainly caused by inadequate clipping values. We propose four
modifications to the conventional BP decoding algorithm to mitigate this error
floor behavior, demonstrating that the error floor is a decoder property, and
not a code property. The results agree with the fact that polar codes are
theoretically proven to not suffer from error floors. Finally, we show that
another cause of error floors can be an improper selection of frozen bit
positions.Comment: ISWCS201
Belief Propagation List Decoding of Polar Codes
We propose a belief propagation list (BPL) decoder with comparable
performance to the successive cancellation list (SCL) decoder of polar codes,
which already achieves the maximum likelihood (ML) bound of polar codes for
sufficiently large list size . The proposed decoder is composed of multiple
parallel independent belief propagation (BP) decoders based on differently
permuted polar code factor graphs. A list of possible transmitted codewords is
generated and the one closest to the received vector, in terms of Euclidean
distance, is picked. To the best of our knowledge, the proposed BPL decoder
provides the best performance of plain polar codes under iterative decoding
known so far. The proposed algorithm does not require any changes in the polar
code structure itself, rendering the BPL into an alternative to the SCL
decoder, equipped with a soft output capability enabling, e.g., iterative
detection and decoding to further improve performance. Further benefits are
lower decoding latency compared to the SCL decoder and the possibility of high
throughput implementations. Additionally, we show that a different selection
strategy of frozen bit positions can further enhance the error-rate performance
of the proposed decoder
Sparse Graphs for Belief Propagation Decoding of Polar Codes
We describe a novel approach to interpret a polar code as a low-density
parity-check (LDPC)-like code with an underlying sparse decoding graph. This
sparse graph is based on the encoding factor graph of polar codes and is
suitable for conventional belief propagation (BP) decoding. We discuss several
pruning techniques based on the check node decoder (CND) and variable node
decoder (VND) update equations, significantly reducing the size (i.e., decoding
complexity) of the parity-check matrix. As a result, iterative polar decoding
can then be conducted on a sparse graph, akin to the traditional
well-established LDPC decoding, e.g., using a fully parallel sum-product
algorithm (SPA). This facilitates the systematic analysis and design of polar
codes using the well-established tools known from analyzing LDPC codes. We show
that the proposed iterative polar decoder has a negligible performance loss for
short-to-intermediate codelengths compared to Arikan's original BP decoder.
Finally, the proposed decoder is shown to benefit from both reduced complexity
and reduced memory requirements and, thus, is more suitable for hardware
implementations.Comment: IEEE International Symposium on Information Theory (ISIT) 201
Decoder-tailored Polar Code Design Using the Genetic Algorithm
We propose a new framework for constructing polar codes (i.e., selecting the
frozen bit positions) for arbitrary channels, and tailored to a given decoding
algorithm, rather than based on the (not necessarily optimal) assumption of
successive cancellation (SC) decoding. The proposed framework is based on the
Genetic Algorithm (GenAlg), where populations (i.e., collections) of
information sets evolve successively via evolutionary transformations based on
their individual error-rate performance. These populations converge towards an
information set that fits both the decoding behavior and the defined channel.
Using our proposed algorithm over the additive white Gaussian noise (AWGN)
channel, we construct a polar code of length 2048 with code rate 0.5, without
the CRC-aid, tailored to plain successive cancellation list (SCL) decoding,
achieving the same error-rate performance as the CRC-aided SCL decoding, and
leading to a coding gain of 1 dB at BER of . Further, a belief
propagation (BP)-tailored construction approaches the SCL error-rate
performance without any modifications in the decoding algorithm itself. The
performance gains can be attributed to the significant reduction in the total
number of low-weight codewords. To demonstrate the flexibility, coding gains
for the Rayleigh channel are shown under SCL and BP decoding. Besides
improvements in error-rate performance, we show that, when required, the GenAlg
can be also set up to reduce the decoding complexity, e.g., the SCL list size
or the number of BP iterations can be reduced, while maintaining the same
error-rate performance.Comment: This work has been submitted to the IEEE for possible publication.
Manuscript submitted September 20, 2018; revised January 28, 2019; date of
current version January 28, 2019. arXiv admin note: substantial text overlap
with arXiv:1901.0644
TC: Throughput Centric Successive Cancellation Decoder Hardware Implementation for Polar Codes
This paper presents a hardware architecture of fast simplified successive
cancellation (fast-SSC) algorithm for polar codes, which significantly reduces
the decoding latency and dramatically increases the throughput.
Algorithmically, fast-SSC algorithm suffers from the fact that its decoder
scheduling and the consequent architecture depends on the code rate; this is a
challenge for rate-compatible system. However, by exploiting the
homogeneousness between the decoding processes of fast constituent polar codes
and regular polar codes, the presented design is compatible with any rate. The
scheduling plan and the intendedly designed process core are also described.
Results show that, compared with the state-of-art decoder, proposed design can
achieve at least 60% latency reduction for the codes with length N = 1024. By
using Nangate FreePDK 45nm process, proposed design can reach throughput up to
5.81 Gbps and 2.01 Gbps for (1024, 870) and (1024, 512) polar code,
respectively.Comment: submitted to ICASSP 201
Joint Source-Channel Decoding of Polar Codes for Language-Based Source
We exploit the redundancy of the language-based source to help polar
decoding. By judging the validity of decoded words in the decoded sequence with
the help of a dictionary, the polar list decoder constantly detects erroneous
paths after every few bits are decoded. This path-pruning technique based on
joint decoding has advantages over stand-alone polar list decoding in that most
decoding errors in early stages are corrected. In order to facilitate the joint
decoding, we first propose a construction of dynamic dictionary using a trie
and show an efficient way to trace the dictionary during decoding. Then we
propose a joint decoding scheme of polar codes taking into account both
information from the channel and the source. The proposed scheme has the same
decoding complexity as the list decoding of polar codes. A list-size adaptive
joint decoding is further implemented to largely reduce the decoding
complexity. We conclude by simulation that the joint decoding schemes
outperform stand-alone polar codes with CRC-aided successive cancellation list
decoding by over 0.6 dB.Comment: Single column, 20 pages, 8 figures, to be submitted to ISIT 201
Fast List Decoders for Polar Codes
Polar codes asymptotically achieve the symmetric capacity of memoryless
channels, yet their error-correcting performance under successive-cancellation
(SC) decoding for short and moderate length codes is worse than that of other
modern codes such as low-density parity-check (LDPC) codes. Of the many methods
to improve the error-correction performance of polar codes, list decoding
yields the best results, especially when the polar code is concatenated with a
cyclic redundancy check (CRC). List decoding involves exploring several
decoding paths with SC decoding, and therefore tends to be slower than SC
decoding itself, by an order of magnitude in practical implementations. In this
paper, we present a new algorithm based on unrolling the decoding tree of the
code that improves the speed of list decoding by an order of magnitude when
implemented in software. Furthermore, we show that for software-defined radio
applications, our proposed algorithm is faster than the fastest software
implementations of LDPC decoders in the literature while offering comparable
error-correction performance at similar or shorter code lengths.Comment: to appear in the IEEE Journal on Selected Areas in Communications -
Special Issue on Recent Advances In Capacity Approaching Codes, 201
A 5.16Gbps decoder ASIC for Polar Code in 16nm FinFET
Polar codes has been selected as 5G standard. However, only a couple of ASIC
featuring decoders are fabricated,and none of them support list size L > 4 and
code length N > 1024. This paper presents an ASIC implementation of three
decoders for polar code: successive cancellation (SC) decoder, flexible decoder
and ultra-reliable decoder. These decoders are all SC based decoder, supporting
list size up to 1,8,32 and code length up to 2^15,2^14,2^11 respectively. This
chip is fabricated in a 16nm TSMC FinFET technology, and can be clocked at 1
Ghz. Optimization techniques are proposed and employed to increase throughput.
Experiment result shows that the throughput can achieve up to 5.16Gbps.
Compared with fabricated AISC decoder and synthesized decoder in literature,
the flexible decoder achieves higher area efficiency
Deep Learning Methods for Improved Decoding of Linear Codes
The problem of low complexity, close to optimal, channel decoding of linear
codes with short to moderate block length is considered. It is shown that deep
learning methods can be used to improve a standard belief propagation decoder,
despite the large example space. Similar improvements are obtained for the
min-sum algorithm. It is also shown that tying the parameters of the decoders
across iterations, so as to form a recurrent neural network architecture, can
be implemented with comparable results. The advantage is that significantly
less parameters are required. We also introduce a recurrent neural decoder
architecture based on the method of successive relaxation. Improvements over
standard belief propagation are also observed on sparser Tanner graph
representations of the codes. Furthermore, we demonstrate that the neural
belief propagation decoder can be used to improve the performance, or
alternatively reduce the computational complexity, of a close to optimal
decoder of short BCH codes.Comment: Accepted To IEEE Journal Of Selected Topics In Signal Processin
Multilevel LDPC Lattices with Efficient Encoding and Decoding and a Generalization of Construction D'
Lattice codes are elegant and powerful structures that not only can achieve
the capacity of the AWGN channel but are also a key ingredient to many
multiterminal schemes that exploit linearity properties. However, constructing
lattice codes that can realize these benefits with low complexity is still a
challenging problem. In this paper, efficient encoding and decoding algorithms
are proposed for multilevel binary LDPC lattices constructed via Construction
D' whose complexity is linear in the total number of coded bits. Moreover, a
generalization of Construction D' is proposed that relaxes some of the nesting
constraints on the parity-check matrices of the component codes, leading to a
simpler and improved design. Based on this construction, low-complexity
multilevel LDPC lattices are designed whose performance under multistage
decoding is comparable to that of polar lattices and close to that of
low-density lattice codes (LDLC) on the power-unconstrained AWGN channel.Comment: 15 pages, 4 figures. To appear in IEEE Transactions on Information
Theor
- …