30 research outputs found
Deriving Good LDPC Convolutional Codes from LDPC Block Codes
Low-density parity-check (LDPC) convolutional codes are capable of achieving
excellent performance with low encoding and decoding complexity. In this paper
we discuss several graph-cover-based methods for deriving families of
time-invariant and time-varying LDPC convolutional codes from LDPC block codes
and show how earlier proposed LDPC convolutional code constructions can be
presented within this framework. Some of the constructed convolutional codes
significantly outperform the underlying LDPC block codes. We investigate some
possible reasons for this "convolutional gain," and we also discuss the ---
mostly moderate --- decoder cost increase that is incurred by going from LDPC
block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010;
revised August 2010, revised November 2010 (essentially final version).
(Besides many small changes, the first and second revised versions contain
corrected entries in Tables I and II.
Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC)
codes are known to be asymptotically good, in the sense that the minimum free
distance grows linearly with the constraint length. In this paper, we use a
protograph-based analysis of terminated LDPCC codes to obtain an upper bound on
the free distance growth rate of ensembles of periodically time-varying LDPCC
codes. This bound is compared to a lower bound and evaluated numerically. It is
found that, for a sufficiently large period, the bounds coincide. This approach
is then extended to obtain bounds on the trapping set numbers, which define the
size of the smallest, non-empty trapping sets, for these asymptotically good,
periodically time-varying LDPCC code ensembles.Comment: To be presented at the 2011 IEEE International Symposium on
Information Theor
A Novel Blind Adaptive Beamformer with Robustness against Mutual Coupling and Miscalibration Effects
Beamforming techniques utilized either at the transmitter or the receiver
terminals have achieved superior quality-of-service performances from both the
multi-antenna wireless communications systems, communications intelligence and
radar target detection perspectives. Despite the overwhelming advantages in
ideal operating conditions, beamforming approaches have been shown to face
substantial performance degradations due to unknown mutual coupling effects and
miscalibrated array elements. As a promising solution, blind beamformers have
been proposed as a class of receiver beamformers that do not require a
reference signal to operate. In this paper, a novel gradient-based blind
beamformer is introduced with the aim of mitigating the deteriorating effects
of unknown mutual coupling or miscalibration effects. The proposed approach is
shown to find the optimal weights in different antenna array configurations in
the presence of several unknown imperfections (e.g., mutual coupling effects,
miscalibration effects due to gain and phase variations, inaccurate antenna
positions). By providing numerical results related to the proposed algorithm
for different array configurations, and bench-marking with the other existing
approaches, the proposed scheme has been shown to achieve superior performance
in many aspects. Additionally, a measurement-based analysis has been included
with validation purposes.Comment: Presented in EuCAP 2023, Copyright IEE
On the Block Error Rate Performance of Spatially Coupled LDPC Codes for Streaming Applications
In this paper, we study the block error rate (BLER) performance of spatially coupled low-density parity-check (SC- LDPC) codes using a sliding window decoder suited for streaming applications. Previous studies of SC-LDPC have focused on the bit error rate (BER) performance or the frame error rate (FER) performance over the entire length of the code. Here, we consider protograph-based constructions of SC-LDPC codes in which a window decoder continuously outputs blocks in a streaming fashion, and we examine the BLER associated with these blocks.We begin by examining the effect of protograph design on the streaming BLER by varying the block size and the coupling width in such a way that the overall constraint length of the SC-LDPC code remains constant. Next, we investigate the BLER scaling behavior with block size and coupling width. Lastly, we consider the effect of employing an outer code to protect blocks, so that small numbers of residual errors can be corrected by the outer code. Simulation results for the additive white Gaussian noise channel (AWGNC) are included and comparisons are made to LDPC block codes (LDPC-BCs)
Randomly Punctured Spatially Coupled LDPC Codes
In this paper, we study random puncturing of protograph-based spatially coupled low-density parity-check (SC- LDPC) code ensembles. We show that, with respect to iterative decoding threshold, the strength and suitability of an LDPC code ensemble for random puncturing over the binary erasure channel (BEC) is completely determined by a single constant that depends only on the rate and iterative decoding threshold of the mother code ensemble. We then use this analysis to show that randomly punctured SC-LDPC code ensembles display near capacity thresholds for a wide range of rates. We also perform an asymptotic minimum distance analysis and show that, like the SC-LDPC mother code ensemble, the punctured SC-LDPC code ensembles are also asymptotically good. Finally, we present some simulation results that confirm the excellent decoding performance promised by the asymptotic results
Randomly Punctured LDPC Codes
In this paper, we present a random puncturing analysis of low-density parity-check (LDPC) code ensembles. We derive a simple analytic expression for the iterative belief propagation (BP) decoding threshold of a randomly punctured LDPC code ensemble on the binary erasure channel (BEC) and show that, with respect to the BP threshold, the strength and suitability of an LDPC code ensemble for random puncturing is completely determined by a single constant that depends only on the rate and the BP threshold of the mother code ensemble. We then provide an efficient way to accurately predict BP thresholds of randomly punctured LDPC code ensembles on the binary- input additive white Gaussian noise channel (BI-AWGNC), given only the BP threshold of the mother code ensemble on the BEC and the design rate, and we show how the prediction can be improved with knowledge of the BI-AWGNC threshold. We also perform an asymptotic minimum distance analysis of randomly punctured code ensembles and present simulation results that confirm the robust decoding performance promised by the asymptotic results. Protograph-based LDPC block code and spatially coupled LDPC code ensembles are used throughout as examples to demonstrate the results
Reduced Complexity Window Decoding Schedules for Coupled LDPC Codes
Window decoding schedules are very attractive for message passing decoding of spatially coupled LDPC codes. They take advantage of the inherent convolutional code structure and allow continuous transmission with low decoding latency and complexity. In this paper we show that the decoding complexity can be further reduced if suitable message passing schedules are applied within the decoding window. An improvement based schedule is presented that easily adapts to different ensemble structures, window sizes, and channel parameters. Its combination with a serial (on-demand) schedule is also considered. Results from a computer search based schedule are shown for comparison