Mothi Venkatesan, Sabaresan (2007-08). Exit charts based analysis and design of rateless codes for the erasure and Gaussian channels. Master's Thesis. Thesis uri icon

abstract

  • Luby Transform Codes were the first class of universal erasure codes introduced to fully realize the concept of scalable and fault-tolerant distribution of data over computer networks, also called Digital Fountain. Later Raptor codes, a generalization of the LT codes were introduced to trade off complexity with performance. In this work, we show that an even broader class of codes exists that are near optimal for the erasure channel and that the Raptor codes form a special case. More precisely, Raptorlike codes can be designed based on an iterative (joint) decoding schedule wherein information is transferred between the LT decoder and an outer decoder in an iterative manner. The design of these codes can be formulated as a LP problem using EXIT Charts and density evolution. In our work, we show the existence of codes, other than the Raptor codes, that perform as good as the existing ones. We extend this framework of joint decoding of the component codes to the additive white Gaussian noise channels and introduce the design of Rateless codes for these channels. Under this setting, for asymptotic lengths, it is possible to design codes that work for a class of channels defined by the signal-to-noise ratio. In our work, we show that good profiles can be designed using density evolution and Gaussian approximation. EXIT charts prove to be an intuitive tool and aid in formulating the code design problem as a LP problem. EXIT charts are not exact because of the inherent approximations. Therefore, we use density evolution to analyze the performance of these codes. In the Gaussian case, we show that for asymptotic lengths, a range of designs of Rateless codes exists to choose from based on the required complexity and the overhead. Moreover, under this framework, we can design incrementally redundant schemes for already existing outer codes to make the communication system more robust to channel noise variations.
  • Luby Transform Codes were the first class of universal erasure codes introduced
    to fully realize the concept of scalable and fault-tolerant distribution of data over
    computer networks, also called Digital Fountain. Later Raptor codes, a generalization of
    the LT codes were introduced to trade off complexity with performance. In this work,
    we show that an even broader class of codes exists that are near optimal for the
    erasure channel and that the Raptor codes form a special case. More precisely, Raptorlike
    codes can be designed based on an iterative (joint) decoding schedule wherein
    information is transferred between the LT decoder and an outer decoder in an iterative
    manner. The design of these codes can be formulated as a LP problem using EXIT Charts
    and density evolution. In our work, we show the existence of codes, other than the
    Raptor codes, that perform as good as the existing ones.
    We extend this framework of joint decoding of the component codes to the
    additive white Gaussian noise channels and introduce the design of Rateless codes for
    these channels. Under this setting, for asymptotic lengths, it is possible to design codes
    that work for a class of channels defined by the signal-to-noise ratio. In our work, we
    show that good profiles can be designed using density evolution and Gaussian
    approximation. EXIT charts prove to be an intuitive tool and aid in formulating the code
    design problem as a LP problem. EXIT charts are not exact because of the inherent
    approximations. Therefore, we use density evolution to analyze the performance of these codes. In the Gaussian case, we show that for asymptotic lengths, a range of
    designs of Rateless codes exists to choose from based on the required complexity and
    the overhead.
    Moreover, under this framework, we can design incrementally redundant
    schemes for already existing outer codes to make the communication system more
    robust to channel noise variations.

publication date

  • August 2007