A New Design Framework for LT Codes over
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Luby transform (LT) codes [2] were the first practical realization of such rateless codes and shown to be universal for transmission over the binary erasure channel. However the complexity and delay grow fast with increasing information block length. Furthermore, an LT code can be considered as a sequence of irregular non-systematic low-density generator matrix (LDGM) codes [3], and therefore such a code exhibits a high error floor for transmission over noisy channels due to poor minimum-distance properties. This error floor does not diminish with increasing information block length [4]. Particularly, it was demonstrated that bit error rate (BER) and word error rate (WER) performances of LT codes over binary symmetric channels and binary-input additive white Gaussian noise (AWGN) channels exhibit high error floors [5], [6].
2014 IEEE International Symposium on Information Theory
A New Design Framework for LT Codes over
Noisy Channels
Iqbal Hussain∗, Ingmar Land†, Terence H. Chan†, Ming Xiao∗, Lars K. Rasmussen∗ ∗KTH Royal Institute of Technology and the ACCESS Linnaeus Center Stockholm, Sweden {iqbalh, mingx, lkra}@kth.se †Institute for Telecommunications Research, University of South Australia Adelaide, Australia{nd,terence.chan}@.au
For scenarios where CSI is not available at the transmitter, rateless codes with fixed degree distributions were proposed
The work is supported by the LM Ericssons stiftelse fo¨r fra¨mjande av elektroteknisk forskning, and the MC-IRSES TEASCONE project 2012318970.
To demonstrate the framework we consider an LT code optimized for low complexity. The decoding complexity of an LT code is relatively low for transmission over erasure channels. However, decoding complexity can be a major concern for noisy channels, in particular with complexity- and latencyconstrained applications. The average encoding and decoding complexity of LT codes depends on the average variableand check-node degrees. Here, we optimize an LT code for minimizing the average check-node degree and subsequently the average variable-node degree to obtain low-complexity LT codes. Minimizing the average check- and variable-node degree reduces the overall complexity.
In the present paper, we propose a generalized encoding scheme to accommodate rate-compatible degree distributions. We further provide a design framework based on extrinsic information (EXIT) chart analysis [8] to obtain dynamic check- and variable-node degree distributions for transmission over noisy channels. Using ideas from EXIT-chart design for irregular LDPC codes [9], degree distributions are optimized for LT codes under constraints to ensure rate-compatibility. This generalized framework can be exploited for improved performance, limited complexity or low delay depending on application requirements. We focus on LT-coded transmission over AWGN channels; the extension to other channels is possible.
in [2], [4]–[6]. The concept of reconfigurable rateless codes was proposed in [7], where it was observed that the optimal check-node degree distribution changes with the instantaneous signal-to-noise ratio (SNR): the check-node degree distribution is adapted to the instantaneous SNR, which is estimated based on the lack of acknowledgement (ACK) feedback. However, this approach is used only to maximize the code rate under bad channel conditions.
I. INTRODUCTION
The concept of digital fountain codes was introduced in [1] as an efficient approach for reliable multicast transmission over the packet erasure channel. For such codes the rate is not fixed prior to transmission; instead an unlimited number of parity bits can be generated on-the-fly to adapt to fluctuating channel conditions without requiring channel state information (CSI) at the transmitter. The rateless property enables seamless adaptation to transmission over time-varying channels.
Abstract—Luby transform (LT) codes are a class of rateless codes that automatically adapt their rate to the quality of the communication channel. In the original LT codes, fixed checknode degree distributions are used to combine variable nodes uniformly at random to extend the code graph and produce code bits. Here we propose a different approach: we design a sequence of rate-compatible degree distributions, and develop an algorithm that produces code bits in a manner such that the resulting degree distributions follow the designed sequence. Using this new design framework, we develop low-complexity LT codes suitable for time-varying noisy channels. Performance and complexity of the proposed LT codes are measured in terms of bit error rate and average number of edges per information and coded bit, respectively. Numerical examples illustrate the resulting trade-off between performance and complexity of the designed LT codes.
2014 IEEE International Symposium on Information Theory
A New Design Framework for LT Codes over
Noisy Channels
Iqbal Hussain∗, Ingmar Land†, Terence H. Chan†, Ming Xiao∗, Lars K. Rasmussen∗ ∗KTH Royal Institute of Technology and the ACCESS Linnaeus Center Stockholm, Sweden {iqbalh, mingx, lkra}@kth.se †Institute for Telecommunications Research, University of South Australia Adelaide, Australia{nd,terence.chan}@.au
For scenarios where CSI is not available at the transmitter, rateless codes with fixed degree distributions were proposed
The work is supported by the LM Ericssons stiftelse fo¨r fra¨mjande av elektroteknisk forskning, and the MC-IRSES TEASCONE project 2012318970.
To demonstrate the framework we consider an LT code optimized for low complexity. The decoding complexity of an LT code is relatively low for transmission over erasure channels. However, decoding complexity can be a major concern for noisy channels, in particular with complexity- and latencyconstrained applications. The average encoding and decoding complexity of LT codes depends on the average variableand check-node degrees. Here, we optimize an LT code for minimizing the average check-node degree and subsequently the average variable-node degree to obtain low-complexity LT codes. Minimizing the average check- and variable-node degree reduces the overall complexity.
In the present paper, we propose a generalized encoding scheme to accommodate rate-compatible degree distributions. We further provide a design framework based on extrinsic information (EXIT) chart analysis [8] to obtain dynamic check- and variable-node degree distributions for transmission over noisy channels. Using ideas from EXIT-chart design for irregular LDPC codes [9], degree distributions are optimized for LT codes under constraints to ensure rate-compatibility. This generalized framework can be exploited for improved performance, limited complexity or low delay depending on application requirements. We focus on LT-coded transmission over AWGN channels; the extension to other channels is possible.
in [2], [4]–[6]. The concept of reconfigurable rateless codes was proposed in [7], where it was observed that the optimal check-node degree distribution changes with the instantaneous signal-to-noise ratio (SNR): the check-node degree distribution is adapted to the instantaneous SNR, which is estimated based on the lack of acknowledgement (ACK) feedback. However, this approach is used only to maximize the code rate under bad channel conditions.
I. INTRODUCTION
The concept of digital fountain codes was introduced in [1] as an efficient approach for reliable multicast transmission over the packet erasure channel. For such codes the rate is not fixed prior to transmission; instead an unlimited number of parity bits can be generated on-the-fly to adapt to fluctuating channel conditions without requiring channel state information (CSI) at the transmitter. The rateless property enables seamless adaptation to transmission over time-varying channels.
Abstract—Luby transform (LT) codes are a class of rateless codes that automatically adapt their rate to the quality of the communication channel. In the original LT codes, fixed checknode degree distributions are used to combine variable nodes uniformly at random to extend the code graph and produce code bits. Here we propose a different approach: we design a sequence of rate-compatible degree distributions, and develop an algorithm that produces code bits in a manner such that the resulting degree distributions follow the designed sequence. Using this new design framework, we develop low-complexity LT codes suitable for time-varying noisy channels. Performance and complexity of the proposed LT codes are measured in terms of bit error rate and average number of edges per information and coded bit, respectively. Numerical examples illustrate the resulting trade-off between performance and complexity of the designed LT codes.
