2 research outputs found
Systematic Block Markov Superposition Transmission of Repetition Codes
In this paper, we propose systematic block Markov superposition transmission
of repetition~(BMST-R) codes, which can support a wide range of code rates but
maintain essentially the same encoding/decoding hardware structure. The
systematic BMST-R codes resemble the classical rate-compatible punctured
convolutional~(RCPC) codes, except that they are typically non-decodable by the
Viterbi algorithm due to the huge constraint length induced by the
block-oriented encoding process. The information sequence is partitioned
equally into blocks and transmitted directly, while their replicas are
interleaved and transmitted in a block Markov superposition manner. By taking
into account that the codes are systematic, we derive both upper and lower
bounds on the bit-error-rate~(BER) under maximum {\em a posteriori}~(MAP)
decoding. The derived lower bound reveals connections among BER, encoding
memory and code rate, which provides a way to design good systematic BMST-R
codes and also allows us to make trade-offs among efficiency, performance and
complexity. Numerical results show that:~1)~the proposed bounds are tight in
the high signal-to-noise ratio~(SNR) region;~2)~systematic BMST-R codes perform
well in a wide range of code rates, and~3)~systematic BMST-R codes outperform
spatially coupled low-density parity-check~(SC-LDPC) codes under an equal
decoding latency constraint.Comment: Submitted to IEEE Trans. Inf. Theor
Systematic Convolutional Low Density Generator Matrix Code
In this paper, we propose a systematic low density generator matrix (LDGM)
code ensemble, which is defined by the Bernoulli process. We prove that, under
maximum likelihood (ML) decoding, the proposed ensemble can achieve the
capacity of binary-input output symmetric (BIOS) memoryless channels in terms
of bit error rate (BER). The proof technique reveals a new mechanism, different
from lowering down frame error rate (FER), that the BER can be lowered down by
assigning light codeword vectors to light information vectors. The finite
length performance is analyzed by deriving an upper bound and a lower bound,
both of which are shown to be tight in the high signal-to-noise ratio (SNR)
region. To improve the waterfall performance, we construct the systematic
convolutional LDGM (SC-LDGM) codes by a random splitting process. The SC-LDGM
codes are easily configurable in the sense that any rational code rate can be
realized without complex optimization. As a universal construction, the main
advantage of the SC-LDGM codes is their near-capacity performance in the
waterfall region and predictable performance in the error-floor region that can
be lowered down to any target as required by increasing the density of the
uncoupled LDGM codes. Numerical results are also provided to verify our
analysis.Comment: submitted to IEEE Transactions on Information Theor