Performance-complexity tradeoffs of rateless codes

Abstract

In this thesis, we analyze tradeoffs of rateless codes between performance and complexity in general noisy channels. While for erasure channels a decoder only needs to use unerased received symbols, for noisy channel the decoder needs to take all received symbols into account because each of them contains some information about the trasmitted message. This, however, increases complexity since more processing is needed. To reduce the complexity, the decoder can discard some unreliable symbols. This results in a performance-complexity tradeoff. In addition, we consider a scenario where a rateless code operates over a fixed-rate error correcting code with reliable error checking such that the rateless code sees an erasure channel, which is typically used in practice for wireless applications, e.g., in 3GPP MBMS and DVB-H. At the receiver, only succesfully decoded blocks by the fixed-rate code are forwarded to the rateless code decoder. If some soft information of decoded blocks having errors is also forwarded, it can help decode message blocks better. Then the receiver can decode the message blocks with less received blocks. However, this has a drawback since more processing is inevitable and complexity will be higher. This results in another type of performance-complexity tradeoff. We study the performance-complexity tradeoffs of rateless codes for the two cases. We consider AWGN and fading channels with binary input. We show the optimal tradeoff, and further demonstrate usefulness of the tradeoff by analyzing codes approaching the optimal one closely. We also design good LDPC codes which is suitable as the underlying fixed-rate code in the second scenario by using iterative linear programming and density evolution.