7 research outputs found
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
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
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
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