Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTransmit Correlation Diversity: Generalization, New Techniques, and Improved Bounds
57
0
0.0
(
0
)
Added by
Aria Nosratinia
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. This idea was conceived for channels in which transmit correlation matrices have mutually exclusive eigenspaces, allowing non-interfering training and transmission. This paper broadens the scope of transmit correlation diversity to the case of partially and fully overlapping eigenspaces and introduces techniques to harvest these generalized gains. For the two-user MIMO broadcast channel, we derive achievable degrees of freedom (DoF) and achievable rate regions with/without channel state information at the receiver (CSIR). When CSIR is available, the proposed achievable DoF region is tight in some configurations of the number of receive antennas and the channel correlation ranks. We then extend the DoF results to the $K$-user case by analyzing the interference graph that characterizes the overlapping structure of the eigenspaces. Our achievability results employ a combination of product superposition in the common part of the eigenspaces, and pre-beamforming (rate splitting) to create multiple data streams in non-overlapping parts of the eigenspaces. Massive MIMO is a natural example in which spatially correlated link gains are likely to occur. We study the achievable downlink sum rate for a frequency-division duplex massive MIMO system under transmit correlation diversity.
rate research
Read More
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation) results are known, leaving gaps between the best known constructions and best known lower bounds. Towards determining the optimal redundancy of batch codes, we prove a new lower bound on the redundancy of batch codes. Specifically, we study (primitive, multiset) linear batch codes that systematically encode $n$ information symbols into $N$ codeword symbols, with the requirement that any multiset of $k$ symbol requests can be obtained in disjoint ways. We show that such batch codes need $Omega(sqrt{Nk})$ symbols of redundancy, improving on the previous best lower bounds of $Omega(sqrt{N}+k)$ at all $k=n^varepsilon$ with $varepsilonin(0,1)$. Our proof follows from analyzing the dimension of the order-$O(k)$ tensor of the batch codes dual code.
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average length and exponential-average redundancy. The first of these relates to various problems involving queueing, uncertainty, and lossless communications, and it can be reduced to the second, which has properties more amenable to analysis. These bounds, some of which are tight, are in terms of a form of entropy and/or the probability of an input symbol, improving on recently discovered bounds of similar form. We also observe properties of optimal codes over the exponential-average redundancy utility.
Total correlation (TC) is a fundamental concept in information theory to measure the statistical dependency of multiple random variables. Recently, TC has shown effectiveness as a regularizer in many machine learning tasks when minimizing/maximizing the correlation among random variables is required. However, to obtain precise TC values is challenging, especially when the closed-form distributions of variables are unknown. In this paper, we introduced several sample-based variational TC estimators. Specifically, we connect the TC with mutual information (MI) and constructed two calculation paths to decompose TC into MI terms. In our experiments, we estimated the true TC values with the proposed estimators in different simulation scenarios and analyzed the properties of the TC estimators.
In this paper we develop a technique to extend any bound for cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes. We use this technique to improve the searching of new bounds for abelian codes.
This paper provides upper and lower bounds on the optimal guessing moments of a random variable taking values on a finite set when side information may be available. These moments quantify the number of guesses required for correctly identifying the unknown object and, similarly to Arikans bounds, they are expressed in terms of the Arimoto-Renyi conditional entropy. Although Arikans bounds are asymptotically tight, the improvement of the bounds in this paper is significant in the non-asymptotic regime. Relationships between moments of the optimal guessing function and the MAP error probability are also established, characterizing the exact locus of their attainable values. The bounds on optimal guessing moments serve to improve non-asymptotic bounds on the cumulant generating function of the codeword lengths for fixed-to-variable optimal lossless source coding without prefix constraints. Non-asymptotic bounds on the reliability function of discrete memoryless sources are derived as well. Relying on these techniques, lower bounds on the cumulant generating function of the codeword lengths are derived, by means of the smooth Renyi entropy, for source codes that allow decoding errors.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
