1,396 research outputs found
Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions
Polar transforms are central operations in the study of polar codes. This
paper examines polar transforms for non-stationary memoryless sources on
possibly infinite source alphabets. This is the first attempt of source
polarization analysis over infinite alphabets. The source alphabet is defined
to be a Polish group, and we handle the Ar{\i}kan-style two-by-two polar
transform based on the group. Defining erasure distributions based on the
normal subgroup structure, we give recursive formulas of the polar transform
for our proposed erasure distributions. As a result, the recursive formulas
lead to concrete examples of multilevel source polarization with countably
infinite levels when the group is locally cyclic. We derive this result via
elementary techniques in lattice theory.Comment: 12 pages, 1 figure, a short version has been accepted by the 2019
IEEE International Symposium on Information Theory (ISIT2019
Secure Multiplex Coding with Dependent and Non-Uniform Multiple Messages
The secure multiplex coding (SMC) is a technique to remove rate loss in the
coding for wire-tap channels and broadcast channels with confidential messages
caused by the inclusion of random bits into transmitted signals. SMC replaces
the random bits by other meaningful secret messages, and a collection of secret
messages serves as the random bits to hide the rest of messages. In the
previous researches, multiple secret messages were assumed to have independent
and uniform distributions, which is difficult to be ensured in practice. We
remove this restrictive assumption by a generalization of the channel
resolvability technique.
We also give practical construction techniques for SMC by using an arbitrary
given error-correcting code as an ingredient, and channel-universal coding of
SMC. By using the same principle as the channel-universal SMC, we give coding
for the broadcast channel with confidential messages universal to both channel
and source distributions.Comment: We made several changes to improve the presentatio
How to Compute Modulo Prime-Power Sums
The problem of computing modulo prime-power sums is investigated in
distributed source coding as well as computation over Multiple-Access Channel
(MAC). We build upon group codes and present a new class of codes called Quasi
Group Codes (QGC). A QGC is a subset of a group code. These codes are not
closed under the group addition. We investigate some properties of QGC's, and
provide a packing and a covering bound. Next, we use these bounds to derived
achievable rates for distributed source coding as well as computation over MAC.
We show that strict improvements over the previously known schemes can be
obtained using QGC's
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