Improving the Left Degree Distribution of Fountain Codes in the Finite-Length Regime
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Authors
Hayajneh, Khaled
Date
2013-08-22
Type
thesis
Language
eng
Keyword
Fountain codes , Left degree distribution (LDD) , LT codes
Alternative Title
Abstract
Fountain codes were introduced to provide higher reliability, lower complexities, and
more scalability for networks such as the Internet. In this thesis, we study Luby-
Transform (LT) codes which are the realization of Fountain codes. In the LT
codes, a sparse random factor graph is dynamically generated on both the encoder
and decoder sides of the communications channel. The graph is generated from an
ensemble degree distribution. The LT codes are also known as rateless codes, in the
sense that they can generate potentially limitless codeword symbols from original data
and self-adjust to channels with different erasure probabilities. LT Codes also have a
very low encoding and decoding complexities when comparing with some traditional
block codes, e.g., Reed Solomon (RS) codes and Low-Density-Parity-Check (LDPC)
codes. Therefore, LT Codes are suitable for many different kinds of applications such
as broadcast transmission. LT codes achieve the capacity of the Binary Erasure Channel (BEC) asymptotically and universally. For finite lengths, the search is continued to nd codes closer to the capacity limits at even lower encoding and decoding complexities. Most previous work on single-layer Fountain coding targets the design via the right degree distribution. The left degree distribution of an LT code is left as Poisson to protect the universality. For finite lengths, this is no longer an issue; thus, we focus on the design of better codes for the BEC and noisy channels as well at practical lengths.
We propose two encoding schemes for BEC and noisy channels by shaping the left
degree distribution. Our left degree shaping provides codes outperforming regular LT
code and all other competing schemes in the literature. For instance, at a bit error
rate of 10_{-7} and k = 256, our scheme provides a realized rate of 0.6 which is 23.5% higher than Sorensen et al.'s scheme over BEC. In addition, over noisy channels
our proposed scheme achieves an improvement of 14% in the released rates at k = 100
and 30 Belief Propagation (BP) iterations.
Description
Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2013-08-22 19:40:59.885
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