Conference Paper

Protograph-Based LDPC Convolutional Codes for Correlated Erasure Channels

Univ. of California San Diego, La Jolla, CA, USA
DOI: 10.1109/ICC.2010.5502364 Conference: Communications (ICC), 2010 IEEE International Conference on
Source: IEEE Xplore


We consider terminated LDPC convolutional codes (LDPC-CC) constructed from photographs and explore the performance of these codes on correlated erasure channels including a single-burst channel (SBC) and Gilbert-Elliott channel (GEC). We consider code performance with a latency-constrained message passing decoder and the belief propagation decoder. We give theoretical bounds on the code efficiency over the SBC and describe a construction that achieves this bound.We show that the designed codes with belief propagation (BP) decoding perform as well as the regular LDPC-CCs presented in the literature on the binary erasure channel (BEC) and the GEC, while achieving significant gains on the SBC. In the case of windowed decoding, our codes perform much better than the best known regular LDPC-CCs over the BEC and the GEC, with very low decoding latencies.

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    • "We study the requirements of LDPC-CC ensembles for good performance over erasure channels with windowed decoding (WD). We are interested in designing ensembles that have good performances over erasure channels with [2] and without [1] memory with both BP and windowed decoding. Although the channels considered here are erasure channels, we note that the WD scheme can be made use of over any channel. "
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    ABSTRACT: We propose a windowed decoding scheme for protograph-based LDPC convolutional codes (LDPC-CC) that allows us to efficiently trade-off decoding performance for gains in latency. We study the performance of regular LDPC-CC with the windowed decoding scheme. In particular, we show that the class of LDPC-CC proposed in the literature with good belief propagation performance is ill-suited for windowed decoding. Further, we establish properties of code ensembles with good windowed decoding performance over erasure channels with and without memory.
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    ABSTRACT: We consider a windowed decoding scheme for LDPC convolutional codes that is based on the belief-propagation (BP) algorithm. We discuss the advantages of this decoding scheme and identify certain characteristics of LDPC convolutional code ensembles that exhibit good performance with the windowed decoder. We will consider the performance of these ensembles and codes over erasure channels with and without memory. We show that the structure of LDPC convolutional code ensembles is suitable to obtain performance close to the theoretical limits over the memoryless erasure channel, both for the BP decoder and windowed decoding. However, the same structure imposes limitations on the performance over erasure channels with memory.
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    ABSTRACT: Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach capacity, as well as for finite lengths, since degree-2 variables that result in high error floors can be completely avoided. However, to realize the promised good performance, one needs large blocklengths. This in turn implies a large latency and decoding complexity. For the memoryless binary erasure channel, we consider the decoding of spatially coupled codes through a windowed decoder that aims to retain many of the attractive features of belief propagation, while trying to reduce complexity further. We characterize the performance of this scheme by defining thresholds on channel erasure rates that guarantee a target erasure rate. We give analytical lower bounds on these thresholds and show that the performance approaches that of belief propagation exponentially fast in the window size. We give numerical results including the thresholds computed using density evolution and the erasure rate curves for finite-length spatially coupled codes.
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