152 research outputs found
Polar codes in network quantum information theory
Polar coding is a method for communication over noisy classical channels
which is provably capacity-achieving and has an efficient encoding and
decoding. Recently, this method has been generalized to the realm of quantum
information processing, for tasks such as classical communication, private
classical communication, and quantum communication. In the present work, we
apply the polar coding method to network quantum information theory, by making
use of recent advances for related classical tasks. In particular, we consider
problems such as the compound multiple access channel and the quantum
interference channel. The main result of our work is that it is possible to
achieve the best known inner bounds on the achievable rate regions for these
tasks, without requiring a so-called quantum simultaneous decoder. Thus, our
work paves the way for developing network quantum information theory further
without requiring a quantum simultaneous decoder.Comment: 18 pages, 2 figures, v2: 10 pages, double column, version accepted
for publicatio
Homologous Codes for Multiple Access Channels
Building on recent development by Padakandla and Pradhan, and by Lim, Feng,
Pastore, Nazer, and Gastpar, this paper studies the potential of structured
nested coset coding as a complete replacement for random coding in network
information theory. The roles of two techniques used in nested coset coding to
generate nonuniform codewords, namely, shaping and channel transformation, are
clarified and illustrated via the simple example of the two-sender multiple
access channel. While individually deficient, the optimal combination of
shaping and channel transformation is shown to achieve the same performance as
traditional random codes for the general two-sender multiple access channel.
The achievability proof of the capacity region is extended to the multiple
access channels with more than two senders, and with one or more receivers. A
quantization argument consistent with the construction of nested coset codes is
presented to prove achievability for their Gaussian counterparts. These results
open up new possibilities of utilizing nested coset codes with the same
generator matrix for a broader class of applications
Broadcast Capacity Region of Two-Phase Bidirectional Relaying
In a three-node network a half-duplex relay node enables bidirectional
communication between two nodes with a spectral efficient two phase protocol.
In the first phase, two nodes transmit their message to the relay node, which
decodes the messages and broadcast a re-encoded composition in the second
phase. In this work we determine the capacity region of the broadcast phase. In
this scenario each receiving node has perfect information about the message
that is intended for the other node. The resulting set of achievable rates of
the two-phase bidirectional relaying includes the region which can be achieved
by applying XOR on the decoded messages at the relay node. We also prove the
strong converse for the maximum error probability and show that this implies
that the [\eps_1,\eps_2]-capacity region defined with respect to the average
error probability is constant for small values of error parameters \eps_1,
\eps_2.Comment: 25 pages, 2 figures, submitted to IEEE Transactions on Information
Theor
Finite-Blocklength and Error-Exponent Analyses for LDPC Codes in Point-to-Point and Multiple Access Communication
This paper applies error-exponent and dispersionstyle analyses to derive finite-blocklength achievability bounds for low-density parity-check (LDPC) codes over the point-to-point channel (PPC) and multiple access channel (MAC). The errorexponent analysis applies Gallager’s error exponent to bound achievable symmetrical and asymmetrical rates in the MAC. The dispersion-style analysis begins with a generalization of the random coding union (RCU) bound from random code ensembles with i.i.d. codewords to random code ensembles in which codewords may be statistically dependent; this generalization is useful since the codewords of random linear codes such as LDPC codes are dependent. Application of the RCU bound yields finiteblocklength error bounds and asymptotic achievability results for both i.i.d. random codes and LDPC codes. For discrete, memoryless channels, these results show that LDPC codes achieve first- and second-order performance that is optimal for the PPC and identical to the best prior results for the MAC
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