41,351 research outputs found
Threshold-Based Fast Successive-Cancellation Decoding of Polar Codes
Fast SC decoding overcomes the latency caused by the serial nature of the SC
decoding by identifying new nodes in the upper levels of the SC decoding tree
and implementing their fast parallel decoders. In this work, we first present a
novel sequence repetition node corresponding to a particular class of bit
sequences. Most existing special node types are special cases of the proposed
sequence repetition node. Then, a fast parallel decoder is proposed for this
class of node. To further speed up the decoding process of general nodes
outside this class, a threshold-based hard-decision-aided scheme is introduced.
The threshold value that guarantees a given error-correction performance in the
proposed scheme is derived theoretically. Analysis and hardware implementation
results on a polar code of length with code rates , , and
show that our proposed algorithm reduces the required clock cycles by up
to , and leads to a improvement in the maximum operating frequency
compared to state-of-the-art decoders without tangibly altering the
error-correction performance. In addition, using the proposed threshold-based
hard-decision-aided scheme, the decoding latency can be further reduced by
at ~dB.Comment: 14 pages, 8 figures, 5 tables, submitted to IEEE Transactions on
Communication
Polar Codes over Fading Channels with Power and Delay Constraints
The inherent nature of polar codes being channel specific makes it difficult
to use them in a setting where the communication channel changes with time. In
particular, to be able to use polar codes in a wireless scenario, varying
attenuation due to fading needs to be mitigated. To the best of our knowledge,
there has been no comprehensive work in this direction thus far. In this work,
a practical scheme involving channel inversion with the knowledge of the
channel state at the transmitter, is proposed. An additional practical
constraint on the permissible average and peak power is imposed, which in turn
makes the channel equivalent to an additive white Gaussian noise (AWGN) channel
cascaded with an erasure channel. It is shown that the constructed polar code
could be made to achieve the symmetric capacity of this channel. Further, a
means to compute the optimal design rate of the polar code for a given power
constraint is also discussed.Comment: 6 pages, 6 figure
Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes
Kudekar et al. recently proved that for transmission over the binary erasure
channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the
coupled ensemble to the MAP threshold of the underlying LDPC codes. One major
drawback of the capacity-achieving spatially-coupled LDPC codes is that one
needs to increase the column and row weight of parity-check matrices of the
underlying LDPC codes.
It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes
achieve the capacity of memoryless binary-input symmetric-output channels under
MAP decoding with bounded column and row weight of the parity-check matrices.
The HA codes and the MN codes are dual codes each other.
The aim of this paper is to present an empirical evidence that
spatially-coupled MN (resp. HA) codes with bounded column and row weight
achieve the capacity of the BEC. To this end, we introduce a spatial coupling
scheme of MN (resp. HA) codes. By density evolution analysis, we will show that
the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close
to the Shannon limit.Comment: Corrected typos in degree distributions \nu and \mu of MN and HA
code
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