120 research outputs found
A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes
Spatially-coupled LDPC codes are known to have excellent asymptotic
properties. Much less is known regarding their finite-length performance. We
propose a scaling law to predict the error probability of finite-length
spatially-coupled ensembles when transmission takes place over the binary
erasure channel. We discuss how the parameters of the scaling law are connected
to fundamental quantities appearing in the asymptotic analysis of these
ensembles and we verify that the predictions of the scaling law fit well to the
data derived from simulations over a wide range of parameters. The ultimate
goal of this line of research is to develop analytic tools for the design of
spatially-coupled LDPC codes under practical constraints
On Doped SC-LDPC Codes for Streaming
In streaming applications, doping improves the performance of spatially-coupled low-density parity-check (SC-LDPC) codes by creating reduced-degree check nodes in the coupled chain. We formulate a scaling law to predict the bit and block error rate of periodically-doped semi-infinite SC-LDPC code ensembles streamed over the binary erasure channel under sliding window decoding for a given finite component block length. The scaling law assumes that with some probability doping is equivalent to full termination and triggers two decoding waves; otherwise, decoding performs as if the coupled chain had not been doped at all. We approximate that probability and use the derived scaling laws to predict the error rates of SC-LDPC code ensembles in the presence of doping. The proposed scaling law provides accurate error rate predictions. We further use it to show that in streaming applications periodic doping can yield higher rates than periodic full termination for the same error-correcting performance
Finite-Length Scaling of Spatially Coupled LDPC Codes Under Window Decoding Over the BEC
We analyze the finite-length performance of spatially coupled low-density
parity-check (SC-LDPC) codes under window decoding over the binary erasure
channel. In particular, we propose a refinement of the scaling law by Olmos and
Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under
full belief propagation (BP) decoding. The refined scaling law models the
decoding process as two independent Ornstein-Uhlenbeck processes, in
correspondence to the two decoding waves that propagate toward the center of
the coupled chain for terminated SC-LDPC codes. We then extend the proposed
scaling law to predict the performance of (terminated) SC-LDPC code ensembles
under the more practical sliding window decoding. Finally, we extend this
framework to predict the bit error rate (BER) and block error rate (BLER) of
SC-LDPC code ensembles. The proposed scaling law yields very accurate
predictions of the FER, BLER, and BER for both full BP and window decoding.Comment: Published in IEEE Transactions on Communications (Early Access). This
paper was presented in part at the IEEE Information Theory Workshop (ITW),
Visby, Sweden, August 2019 (arXiv:1904.10410
Finite-Length Scaling Laws for Spatially-Coupled LDPC Codes
This thesis concerns predicting the finite-length error-correcting performance of spatially-coupled low-density parity-check (SC-LDPC) code ensembles over the binary erasure channel. SC-LDPC codes are a very powerful class of codes; their use in practical communication systems, however, requires the system designer to specify a considerable number of code and decoder parameters, all of which affect both the code’s error-correcting capability and the system’s memory, energy, and latency requirements. Navigating the space of the associated trade-offs is challenging. The aim of the finite-length scaling laws proposed in this thesis is to facilitate code and decoder parameter optimization by providing a way to predict the code’s error-rate performance without resorting to Monte-Carlo simulations for each combination of code/decoder and channel parameters.First, we tackle the problem of predicting the frame, bit, and block error rate of SC-LDPC code ensembles over the binary erasure channel under both belief propagation (BP) decoding and sliding window decoding when the maximum number of decoding iterations is unlimited. The scaling laws we develop provide very accurate predictions of the error rates.Second, we derive a scaling law to accurately predict the bit and block error rate of SC-LDPC code ensembles with doping, a technique relevant for streaming applications for limiting the inherent rate loss of SC-LDPC codes. We then use the derived scaling law for code parameter optimization and show that doping can offer a way to achieve better transmission rates for the same target bit error rate than is possible without doping.Last, we address the most challenging (and most practically relevant) case where the maximum number of decoding iterations is limited, both for BP and sliding window decoding. The resulting predictions are again very accurate.Together, these contributions make finite-length SC-LDPC code and decoder parameter optimization via finite-length scaling laws feasible for the design of practical communication systems
A Refined Scaling Law for Spatially Coupled LDPC Codes Over the Binary Erasure Channel
We propose a refined scaling law to predict the finite-length performance in
the waterfall region of spatially coupled low-density parity-check codes over
the binary erasure channel. In particular, we introduce some improvements to
the scaling law proposed by Olmos and Urbanke that result in a better agreement
between the predicted and simulated frame error rate. We also show how the
scaling law can be extended to predict the bit error rate performance.Comment: Paper accepted to IEEE Information Theory Workshop (ITW) 201
Finite Length Analysis of LDPC Codes
In this paper, we study the performance of finite-length LDPC codes in the
waterfall region. We propose an algorithm to predict the error performance of
finite-length LDPC codes over various binary memoryless channels. Through
numerical results, we find that our technique gives better performance
prediction compared to existing techniques.Comment: Submitted to WCNC 201
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