548 research outputs found
A New Class of Multiple-rate Codes Based on Block Markov Superposition Transmission
Hadamard transform~(HT) as over the binary field provides a natural way to
implement multiple-rate codes~(referred to as {\em HT-coset codes}), where the
code length is fixed but the code dimension can be varied from
to by adjusting the set of frozen bits. The HT-coset codes, including
Reed-Muller~(RM) codes and polar codes as typical examples, can share a pair of
encoder and decoder with implementation complexity of order .
However, to guarantee that all codes with designated rates perform well,
HT-coset coding usually requires a sufficiently large code length, which in
turn causes difficulties in the determination of which bits are better for
being frozen. In this paper, we propose to transmit short HT-coset codes in the
so-called block Markov superposition transmission~(BMST) manner. At the
transmitter, signals are spatially coupled via superposition, resulting in long
codes. At the receiver, these coupled signals are recovered by a sliding-window
iterative soft successive cancellation decoding algorithm. Most importantly,
the performance around or below the bit-error-rate~(BER) of can be
predicted by a simple genie-aided lower bound. Both these bounds and simulation
results show that the BMST of short HT-coset codes performs well~(within one dB
away from the corresponding Shannon limits) in a wide range of code rates
Terminated LDPC Convolutional Codes with Thresholds Close to Capacity
An ensemble of LDPC convolutional codes with parity-check matrices composed
of permutation matrices is considered. The convergence of the iterative belief
propagation based decoder for terminated convolutional codes in the ensemble is
analyzed for binary-input output-symmetric memoryless channels using density
evolution techniques. We observe that the structured irregularity in the Tanner
graph of the codes leads to significantly better thresholds when compared to
corresponding LDPC block codes.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
- …