Search arXiv⌕ Search

arXiv · 0706.2906

Capacity Scaling for MIMO Two-Way Relaying

Abstract

A multiple input multiple output (MIMO) two-way relay channel is considered, where two sources want to exchange messages with each other using multiple relay nodes, and both the sources and relay nodes are equipped with multiple antennas. Both the sources are assumed to have equal number of antennas and have perfect channel state information (CSI) for all the channels of the MIMO two-way relay channel, whereas, each relay node is either assumed to have CSI for its transmit and receive channel (the coherent case) or no CSI for any of the channels (the non-coherent case). The main results in this paper are on the scaling behavior of the capacity region of the MIMO two-way relay channel with increasing number of relay nodes. In the coherent case, the capacity region of the MIMO two-way relay channel is shown to scale linearly with the number of antennas at source nodes and logarithmically with the number of relay nodes. In the non-coherent case, the capacity region is shown to scale linearly with the number of antennas at the source nodes and logarithmically with the signal to noise ratio.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rahul Vaze, Robert W. Heath Jr. 2008-04-07. Capacity Scaling for MIMO Two-Way Relaying. https://arxiv.org/abs/0706.2906

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Encoding Trees: A Method for Producing a Variable-Length Prefix Code From Sets of Arbitrary Size

In this work we formalize a new class of binary trees called encoding trees. We extend this structure in two ways, through labelling to create the class of labelled encoding trees, and pruning to create the class of pruned encoding trees. We discuss how these two extensions can be combined to create the the class of pruned labelled encoding trees. Using the supplementary results that we prove about these classes of trees, we construct a code that uses pruned labelled encoding trees to convert a string of symbols from a sequence of non-empty sets to a binary string. We prove that this code is a variable-length prefix code that can process any valid string of symbols from the given sequence of non-empty sets. Furthermore, we construct a code from the class of pruned labelled encoding trees that goes in the opposite direction, from binary strings to a string of symbols from a sequence of non-empty sets of arbitrary symbols. We prove that this code is also a variable-length prefix code that can process any binary string of any length, provided that the sequence of non-empty sets is sufficiently long. We provide an equation that establishes the minimum sequence length to encode any binary string of a given length, based on that length.

cs.IT↗

From Linear Exact Repair to Mixed-Alphabet Codes: The Bandwidth-Subpacketization Tradeoff of MDS Array Codes

MDS array codes achieve optimal storage efficiency in distributed storage systems, but their repair bandwidth depends critically on the sub-packetization level. While the theoretically optimal repair bandwidth (i.e., cut-set bound) of a high-rate exact-repair MDS array code is attainable with sufficiently large sub-packetization, the fundamental limits for fixed sub-packetization remain poorly understood. We study this problem for centralized linear exact repair of $h$ failures from $d$ helper nodes over a fixed finite field. We show that the rank profile of any linear repair scheme is constrained by two auxiliary mixed-alphabet codes. The first code is formed from the kernels of the helper projections and exists for all repair degrees; the second is formed from their row spaces and applies in the full-helper regime when $d\ge r$. These codes have complementary alphabet profiles, and their size and minimum-distance requirements are forced solely by the MDS property and repair correctness. This gives a unified route from classical coding-theoretic upper bounds to repair-bandwidth lower bounds. As a consequence, we obtain several explicit lower bounds via Singleton, Hamming, Plotkin, and Griesmer arguments, including known bounds as corollaries. We further formulate a Delsarte-type support-enumerator LP for mixed-alphabet codes and give an exact type-compressed implementation. For fixed sub-packetization \(\ell\), this yields a polynomial-time procedure for evaluating the resulting finite-parameter lower bound.

cs.IT↗

Support periods of polynomials and support-primitive decomposition of constacyclic codes over Galois rings

Let \(A=\GR(p^e,r)\) have residue field \(\F_q\), and let \(λ\in A^\times\). We relate coefficient compression of monic divisors of \(X^N-λ\) to support-primitive decomposition of constacyclic codes. At a simple-root length, the support period of every nonconstant monic divisor is preserved at each coefficient precision and equals the order of the multiplicative stabilizer of its root set. For a cyclic Frobenius-orbit polynomial, the multiple equal-difference structure determines its support period, core degree, and least relative degree of an unramified extension over which all its basic-irreducible factors are binomials. Coordinate projections give every constacyclic code over a finite commutative ring a unique maximal interleaving into copies of one support-primitive code. At simple-root lengths over \(A\), the intrinsic period of a code is the greatest common divisor of the periods of its torsion codes. The decomposition yields distance and duality formulas and the arithmetic Singleton bound for free codes. At every length, a nonzero code over \(A\) has the same minimum Hamming distance as its highest torsion code, which gives a refined bound. At repeated-root lengths, identical torsion filtrations can occur with different intrinsic periods, while a class of nonzero codes obtained by substitution from simple-root generators retains the same core and minimum distance. Trace matrices recover the coefficients of basic-irreducible cores using unit pivots, and local Hensel corrections lift compressed factors directly. For \(X^n-1\) with \(p\nmid n\), lifting and output have quasi-linear bit cost in the compressed representation when the arithmetic data and residue factorizations are given.

cs.IT↗