60 research outputs found
On a question of Babadi and Tarokh
In a recent remarkable paper, Babadi and Tarokh proved the "randomness" of
sequences arising from binary linear block codes in the sense of spectral
distribution, provided that their dual distances are sufficiently large.
However, numerical experiments conducted by the authors revealed that Gold
sequences which have dual distance 5 also satisfy such randomness property.
Hence the interesting question was raised as to whether or not the stringent
requirement of large dual distances can be relaxed in the theorem in order to
explain the randomness of Gold sequences. This paper improves their result on
several fronts and provides an affirmative answer to this question
Efficient decoding of some classes of binary cyclic codes beyond the Hartmann-Tzeng bound
International audienceA new bound on the distance of binary cyclic codes is proposed. The approach is based on the representation of a subset of the roots of the generator polynomial by a rational function. A new bound on the minimum distance is proven and several classes of binary cyclic codes are identified. For some classes of codes, this bound is better than the known bounds (e.g. BCH or Hartmann-Tzeng bound). Furthermore, a quadratic-time decoding algorithm up to this new bound is developed
URLLC with Coded Massive MIMO via Random Linear Codes and GRAND
A present challenge in wireless communications is the assurance of
ultra-reliable and low-latency communication (URLLC). While the reliability
aspect is well known to be improved by channel coding with long codewords, this
usually implies using interleavers, which introduce undesirable delay. Using
short codewords is a needed change to minimizing the decoding delay. This work
proposes the combination of a coding and decoding scheme to be used along with
spatial signal processing as a means to provide URLLC over a fading channel.
The paper advocates the use of random linear codes (RLCs) over a massive MIMO
(mMIMO) channel with standard zero-forcing detection and guessing random
additive noise decoding (GRAND). The performance of several schemes is assessed
over a mMIMO flat fading channel. The proposed scheme greatly outperforms the
equivalent scheme using 5G's polar encoding and decoding for signal-to-noise
ratios (SNR) of interest. While the complexity of the polar code is constant at
all SNRs, using RLCs with GRAND achieves much faster decoding times for most of
the SNR range, further reducing latency
URLLC with coded massive MIMO via random linear codes and GRAND
A present challenge in wireless communications is the assurance of ultra-reliable and low-latency communication (URLLC). While the reliability aspect is well known to be improved by channel coding with long codewords, this usually implies using interleavers, which introduce undesirable delay. Using short codewords is a needed change to minimizing the decoding delay. This work proposes the combination of a coding and decoding scheme to be used along with spatial signal processing as a means to provide URLLC over a fading channel. The paper advocates the use of random linear codes (RLCs) over a massive MIMO (mMIMO) channel with standard zero-forcing detection and guessing random additive noise decoding (GRAND). The performance of several schemes is assessed over a mMIMO flat fading channel. The proposed scheme greatly outperforms the equivalent scheme using 5G’s polar encoding and decoding for signal-to-noise ratios (SNR) of interest. While the complexity of the polar code is constant at all SNRs, using RLCs with GRAND achieves much faster decoding times for most of the SNR range, further reducing latency.info:eu-repo/semantics/acceptedVersio
Bit flipping decoding for binary product codes
Error control coding has been used to mitigate the impact of noise on the wireless channel.
Today, wireless communication systems have in their design Forward Error Correction (FEC)
techniques to help reduce the amount of retransmitted data. When designing a coding scheme,
three challenges need to be addressed, the error correcting capability of the code, the decoding
complexity of the code and the delay introduced by the coding scheme. While it is easy to design
coding schemes with a large error correcting capability, it is a challenge finding decoding
algorithms for these coding schemes. Generally increasing the length of a block code increases
its error correcting capability and its decoding complexity.
Product codes have been identified as a means to increase the block length of simpler codes,
yet keep their decoding complexity low. Bit flipping decoding has been identified as simple to
implement decoding algorithm. Research has generally been focused on improving bit flipping
decoding for Low Density Parity Check codes. In this study we develop a new decoding
algorithm based on syndrome checking and bit flipping to use for binary product codes, to
address the major challenge of coding systems, i.e., developing codes with a large error
correcting capability yet have a low decoding complexity. Simulated results show that the
proposed decoding algorithm outperforms the conventional decoding algorithm proposed by P.
Elias in BER and more significantly in WER performance. The algorithm offers comparable
complexity to the conventional algorithm in the Rayleigh fading channel
Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices
Quantum low-density parity-check (QLDPC) codes are promising candidates for
error correction in quantum computers. One of the major challenges in
implementing QLDPC codes in quantum computers is the lack of a universal
decoder. In this work, we first propose to decode QLDPC codes with a belief
propagation (BP) decoder operating on overcomplete check matrices. Then, we
extend the neural BP (NBP) decoder, which was originally studied for suboptimal
binary BP decoding of QLPDC codes, to quaternary BP decoders. Numerical
simulation results demonstrate that both approaches as well as their
combination yield a low-latency, high-performance decoder for several short to
moderate length QLDPC codes.Comment: arXiv admin note: text overlap with arXiv:2212.1024
URLLC with coded massive MIMO via random linear codes and GRAND
A present challenge in wireless communications is the assurance of ultra-reliable and low-latency communication (URLLC). While the reliability aspect is well known to be improved by channel coding with long codewords, this usually implies using interleavers, which introduce undesirable delay. Using short codewords is a needed change to minimizing the decoding delay. This work proposes the combination of a coding and decoding scheme to be used along with spatial signal processing as a means to provide URLLC over a fading channel. The paper advocates the use of random linear codes (RLCs) over a massive MIMO (mMIMO) channel with standard zero-forcing detection and guessing random additive noise decoding (GRAND). The performance of several schemes is assessed over a mMIMO flat fading channel. The proposed scheme greatly outperforms the equivalent scheme using 5G's polar encoding and decoding for signal-to-noise ratios (SNR) of interest. While the complexity of the polar code is constant at all SNRs, using RLCs with GRAND achieves much faster decoding times for most of the SNR range, further reducing latency
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