Related papers: Polar codes for classical-quantum channels
A major challenge in quantum communication is addressing the negative effects of noise on channel capacity, especially for completely depolarizing channels, where information transmission is inherently impossible. The concept of indefinite…
We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances…
Polar codes are the latest breakthrough in coding theory, as they are the first family of codes with explicit construction that provably achieve the symmetric capacity of discrete memoryless channels. Ar{\i}kan's polar encoder and…
We present a method of constructing rate-compatible polar codes that are capacity-achieving with low-complexity sequential decoders. The proposed code construction allows for incremental retransmissions at different rates in order to adapt…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…
Transmission of classical information using quantum objects such as polarized photons is studied. The classical (Shannon) channel capacity and its relation to quantum (von Neumann) channel capacity is investigated for various receiver…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
Consider the problem of constructing a polar code of block length $N$ for the transmission over a given channel $W$. Typically this requires to compute the reliability of all the $N$ synthetic channels and then to include those that are…
Recently, Ar{\i}kan 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…
In this correspondence we present a new proof of Holevo's coding theorem for transmitting classical information through quantum channels, and its strong converse. The technique is largely inspired by Wolfowitz's combinatorial approach using…
This paper considers the design and decoding of polar codes for general classical-quantum (CQ) channels. It focuses on decoding via belief-propagation with quantum messages (BPQM) and, in particular, the idea of paired-measurement BPQM…
Polar codes were recently introduced by Ar\i kan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code…
If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with…
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…
Known strategies for sending bits at the capacity rate over a general channel with classical input and quantum output (a cq channel) require the decoder to implement impractically complicated collective measurements. Here, we show that a…
Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect…
The definition of polar codes given by Arikan is explicit, but the construction complexity is an issue. This is due to the exponential growth in the size of the output alphabet of the bit-channels as the codeword length increases. Tal and…
We provide a generalization of quantum polar codes to quantum channels with qudit-input, achieving the symmetric coherent information of the channel. Our scheme relies on a channel combining and splitting construction, where a two-qudit…
We study an analog of the well-known Gel'fand Pinsker Channel which uses quantum states for the transmission of the data. We consider the case where both the sender's inputs to the channel and the channel states are to be taken from a…
A rateless coding scheme transmits incrementally more and more coded bits over an unknown channel until all the information bits are decoded reliably by the receiver. We propose a new rateless coding scheme based on polar codes, and we show…