Related papers: Analysis of Performance of Linear Analog Codes
Mrs. Gerber's Lemma lower bounds the entropy at the output of a binary symmetric channel in terms of the entropy of the input process. In this paper, we lower bound the output entropy via a different measure of input uncertainty, pertaining…
Tree-based demappers for multiple-input multiple-output (MIMO) detection such as the sphere decoder can achieve near-optimal performance but incur high computational cost due to their sequential nature. In this paper, we propose the…
Linear receivers are an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the information-theoretic performance of MIMO linear receivers in two different…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…
This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on…
We consider linear precoding and decoding in the downlink of a multiuser multiple-input, multiple-output (MIMO) system, wherein each user may receive more than one data stream. We propose several mean squared error (MSE) based criteria for…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
We study the performance of distance-three surface code layouts under realistic multi-parameter noise models. We first calculate their thresholds under depolarizing noise. We then compare a Pauli-twirl approximation of amplitude and phase…
In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…
Recent years have seen the remarkable capabilities of large language models (LLMs) for code generation. Different from existing work that evaluate the correctness of the code generated by LLMs, we propose to further evaluate its efficiency.…
This paper proposes a new family of lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in…
The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
With the involvement of multiple programming languages in modern software development, cross-lingual code clone detection has gained traction within the software engineering community. Numerous studies have explored this topic, proposing…
We construct a class of linear space-time block codes for any number of transmit antennas that have controllable ML decoding complexity with a maximum rate of 1 symbol per channel use. The decoding complexity for $M$ transmit antennas can…
Iterative decoders used for decoding low-density parity-check (LDPC) and moderate-density parity-check (MDPC) codes are not characterized by a deterministic decoding radius and their error rate performance is usually assessed through…
To obtain a better cycle-structure is still a challenge for the low-density parity-check (LDPC) code design. This paper formulates two metrics firstly so that the progressive edge-growth (PEG) algorithm and the approximate cycle extrinsic…
We consider the \emph{two-dimensional range maximum query (2D-RMQ)} problem: given an array $A$ of ordered values, to pre-process it so that we can find the position of the smallest element in the sub-matrix defined by a (user-specified)…