213 research outputs found
Decoding Reed-Muller Codes Using Redundant Code Constraints
The recursive projection-aggregation (RPA) decoding algorithm for Reed-Muller (RM) codes was recently introduced by Ye and Abbe. We show that the RPA algorithm is closely related to (weighted) belief-propagation (BP) decoding by interpreting it as a message-passing algorithm on a factor graph with redundant code constraints. We use this observation to introduce a novel decoder tailored to high-rate RM codes. The new algorithm relies on puncturing rather than projections and is called recursive puncturing-aggregation (RXA). We also investigate collapsed (i.e., non-recursive) versions of RPA and RXA and show some examples where they achieve similar performance with lower decoding complexity
Multi-Factor Pruning for Recursive Projection-Aggregation Decoding of RM Codes
The recently introduced recursive projection aggregation (RPA) decoding
method for Reed-Muller (RM) codes can achieve near-maximum likelihood (ML)
decoding performance. However, its high computational complexity makes its
implementation challenging for time- and resource-critical applications. In
this work, we present a complexity reduction technique called multi-factor
pruning that reduces the computational complexity of RPA significantly. Our
simulation results show that the proposed pruning approach with appropriately
selected factors can reduce the complexity of RPA by up to for
while keeping the comparable error-correcting performance
Pipelined Architecture for Soft-decision Iterative Projection Aggregation Decoding for RM Codes
The recently proposed recursive projection-aggregation (RPA) decoding
algorithm for Reed-Muller codes has received significant attention as it
provides near-ML decoding performance at reasonable complexity for short codes.
However, its complicated structure makes it unsuitable for hardware
implementation. Iterative projection-aggregation (IPA) decoding is a modified
version of RPA decoding that simplifies the hardware implementation. In this
work, we present a flexible hardware architecture for the IPA decoder that can
be configured from fully-sequential to fully-parallel, thus making it suitable
for a wide range of applications with different constraints and resource
budgets. Our simulation and implementation results show that the IPA decoder
has 41% lower area consumption, 44% lower latency, four times higher
throughput, but currently seven times higher power consumption for a code with
block length of 128 and information length of 29 compared to a state-of-the-art
polar successive cancellation list (SCL) decoder with comparable decoding
performance
Hardware Implementation of Iterative Projection-Aggregation Decoding of Reed-Muller Codes
In this work, we present a simplification and a corresponding hardware
architecture for hard-decision recursive projection-aggregation (RPA) decoding
of Reed-Muller (RM) codes. In particular, we transform the recursive structure
of RPA decoding into a simpler and iterative structure with minimal
error-correction degradation. Our simulation results for RM(7,3) show that the
proposed simplification has a small error-correcting performance degradation
(0.005 in terms of channel crossover probability) while reducing the average
number of computations by up to 40%. In addition, we describe the first fully
parallel hardware architecture for simplified RPA decoding. We present FPGA
implementation results for an RM(6,3) code on a Xilinx Virtex-7 FPGA showing
that our proposed architecture achieves a throughput of 171 Mbps at a frequency
of 80 MHz
Semi-Deterministic Subspace Selection for Sparse Recursive Projection-Aggregation Decoding of Reed-Muller Codes
Recursive projection aggregation (RPA) decoding as introduced in [1] is a
novel decoding algorithm which performs close to the maximum likelihood decoder
for short-length Reed-Muller codes. Recently, an extension to RPA decoding,
called sparse multi-decoder RPA (SRPA), has been proposed [2]. The SRPA
approach makes use of multiple pruned RPA decoders to lower the amount of
computations while keeping the performance loss small compared to RPA decoding.
However, the use of multiple sparse decoders again increases the computational
burden. Therefore, the focus is on the optimization of sparse single-decoder
RPA decoding to keep the complexity small. In this paper, a novel method is
proposed, to select subsets of subspaces used in the projection and aggregation
step of SRPA decoding in order to decrease the decoding error probability on
AWGN channels. The proposed method replaces the random selection of subspace
subsets with a semi-deterministic selection method based on a figure of merit
that evaluates the performance of each subspace. Our simulation results show
that the semi-deterministic subspace selection improves the decoding
performance up to compared to SRPA. At the same time, the
complexity of SRPA decoding for RM codes of order is reduced by up to
81% compared to SRPA
Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes
Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a
recursive projection aggregation (RPA) decoder has been proposed, which
achieves a performance that is close to the maximum likelihood decoder for
short-length RM codes. One of its main drawbacks, however, is the large amount
of computations needed. In this paper, we devise a new algorithm to lower the
computational budget while keeping a performance close to that of the RPA
decoder. The proposed approach consists of multiple sparse RPAs that are
generated by performing only a selection of projections in each sparsified
decoder. In the end, a cyclic redundancy check (CRC) is used to decide between
output codewords. Simulation results show that our proposed approach reduces
the RPA decoder's computations up to with negligible performance loss.Comment: 6 pages, 12 figure
On Decoding of Reed-Muller Codes Using a Local Graph Search
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes,
which takes advantage of a graph representation of the code. Vertices of the
considered graph correspond to codewords, with two vertices being connected by
an edge if and only if the Hamming distance between the corresponding codewords
equals the minimum distance of the code. The algorithm uses a greedy local
search to find a node optimizing a metric, e.g. the correlation between the
received vector and the corresponding codeword. In addition, the cyclic
redundancy check can be used to terminate the search as soon as a valid
codeword is found, leading to an improvement in the average computational
complexity of the algorithm. Simulation results for both binary symmetric
channel and additive white Gaussian noise channel show that the presented
decoder approaches the performance of maximum likelihood decoding for RM codes
of length less than 1024 and for the second-order RM codes of length less than
4096. Moreover, it is demonstrated that the considered decoding approach
outperforms state-of-the-art decoding algorithms of RM codes with similar
computational complexity for a wide range of block lengths and rates.Comment: Accepted for Publication in IEEE Transactions on Communications. This
paper has been presented in part at the 2020 IEEE Information Theory Workshop
(https://ieeexplore.ieee.org/document/9457605
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