77 research outputs found
Capacity-Achieving Ensembles of Accumulate-Repeat-Accumulate Codes for the Erasure Channel with Bounded Complexity
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes
which asymptotically achieve capacity on the binary erasure channel (BEC) with
{\em bounded complexity}, per information bit, of encoding and decoding. It
also introduces symmetry properties which play a central role in the
construction of capacity-achieving ensembles for the BEC with bounded
complexity. The results here improve on the tradeoff between performance and
complexity provided by previous constructions of capacity-achieving ensembles
of codes defined on graphs. The superiority of ARA codes with moderate to large
block length is exemplified by computer simulations which compare their
performance with those of previously reported capacity-achieving ensembles of
LDPC and IRA codes. The ARA codes also have the advantage of being systematic.Comment: Submitted to IEEE Trans. on Information Theory, December 1st, 2005.
Includes 50 pages and 13 figure
Low-Floor Tanner Codes via Hamming-Node or RSCC-Node Doping
We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders
Encoders for block-circulant LDPC codes
Methods and apparatus to encode message input symbols in accordance with an accumulate-repeat-accumulate code with repetition three or four are disclosed. Block circulant matrices are used. A first method and apparatus make use of the block-circulant structure of the parity check matrix. A second method and apparatus use block-circulant generator matrices
Performance of Joint Channel and Physical Network Coding Based on Alamouti STBC
This work considers the protograph-coded physical network coding (PNC) based
on Alamouti space-time block coding (STBC) over Nakagami-fading two-way relay
channels, in which both the two sources and relay possess two antennas. We
first propose a novel precoding scheme at the two sources so as to implement
the iterative decoder efficiently at the relay. We further address a simplified
updating rule of the log-likelihood-ratio (LLR) in such a decoder. Based on the
simplified LLR-updating rule and Gaussian approximation, we analyze the
theoretical bit-error-rate (BER) of the system, which is shown to be consistent
with the decoding thresholds and simulated results. Moreover, the theoretical
analysis has lower computational complexity than the protograph extrinsic
information transfer (PEXIT) algorithm. Consequently, the analysis not only
provides a simple way to evaluate the error performance but also facilitates
the design of the joint channel-and-PNC (JCNC) in wireless communication
scenarios.Comment: 6 pages, 4 figures, accpete
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
- …