Polar coding is the most recent encoding scheme in the quest for error correction codes that approaches the Shannon limit, has a simple structure, and admits fast decoders. As such, it is an interesting candidate for the quantum key distribution (QKD) protocol that normally operates at high bit error rates and requires codes that operate near the Shannon limit. This paper describes approaches t...

Reed-Solomon and BCH codes were considered as kernels of polar codes by Mori and Tanaka in [6] and Korada, Şaşoğlu, and Urbanke in [4] to create polar codes with large exponents. For codes of length l ≤ q, Mori and Tanaka showed Reed-Solomon codes give the best possible exponent, where q is the size of the input alphabet. However, considering larger matrices over Fq yields better exponents for ...

Recently, Arıkan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel. In the thesis, we show that decoding algorithm of polar codes, called successive cancellation decoding, can be regarded as belief propagation decoding, which has been used for decoding of low-density parity-...

Explicit coding schemes are proposed to achieve the rate-distortion bound for the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion bound for the binary case. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice con...

Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for the doubly-symmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel c...