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Finite Length Serial Concatenation of SPC codes with Convolutional
Codes
In this work, we extend our previous work in the area of parity
concatenated codes. Better performance can be obtained using serially
concatenated codes (single parity check codes as the outer code,
recursive systematic convolutional codes as the inner code, and
separated by a random interleaver). We evaluate the codes using density
evolution methods. We present a way to design the interleaver to
minimize the correlation between the extrinsic information. The
results show that this parity concatenated code can operate within 0.45
dB of the Shannon limit. Similar to the parity concatenated codes,
these codes are superior in approaching the sphere packing bound. It
can achieve near sphere packing bound decoding for block sizes ranging
from 200 (about 0.8 dB) to 10,000 (within 0.6 dB) information bits.
(All are for a block error rate of $10^{-4}$). The improvement
over the coding schemes in \cite{Wei02} is 0.3-0.4 dB for block
lengths more than 300 bits and over JPL turbo codes is 0.3 dB for block
lengths less than 1000 bits. The peak complexity of the scheme is
higher than the JPL turbo codes, while the average
complexity is comparative. We also propose a reliable error detection
method which makes this coding scheme very attractive
for communications using short packets.
Several Properties of Short LDPC Codes
In this paper,we present several properties on minimum distance (dmin)
and girth (Gmin) in Tanner graphs for LDPC codes with
small left degrees. We show that the distance growth of (2,4) LDPC
codes is too slow to achieve the desired performance. We further give a
tight upper bound on the maximum possible girth. The numerical results
show that codes with large Gmin could outperform the
average performance of regular ensembles of the LDPC codes over binary
symmetric channels. The same codes perform about 1.5 dB away from the
sphere packing bound on AWGN channels.
Construction of Final Length Regular LDPC Codes With Large Girth
In this letter, we present a method that can construct final length
regular LDPC codes with large girth. Let Gu denote the
upper bound on the minimum girth (Gmin) in the above
work. We find (3,6) LDPC codes with Gmin=Gu
for n=16, 64 and 256,
respectively; and Gmin=Gu-2 for n=32,
128, and 512, respectively. The number of variable nodes with Gmin
are 2, 64, 50, 256, 510 and 324 for n=32, 64, 128, 256, 512 and
1024,
respectively. The numerical results show that these codes can perform
within 1.8-2.2 dB of the sphere packing bound on AWGN channels.
download the codes .
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Last modified: Dec, 2003.