Symmetric LDPC codes are not necessarily locally testable
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An important class of modern channel codes is the capacity-achieving sequences of low-density parity-check block codes. Such sequences are usually designed for the binary erasure channel and are decoded by iterative message-passing algorithms. In this pape ...
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Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, ...
A low-density parity check (LDPC) circuit and its properties as a post-processor is proposed for physically unclonable functions (PUFs) applications. PUFs can be realized using process variations or signal noises in SRAM or other PUF circuits, whereas the ...
We consider the dynamics of message passing for spatially coupled codes and, in particular, the set of density evolution equations that tracks the profile of decoding errors along the spatial direction of coupling. It is known that, for suitable boundary c ...
The goal of channel coding is to detect and correct errors that appear during the transmission of information. In the past few decades, channel coding has become an integral part of most communications standards as it improves the energy-efficiency of tran ...
We determine the stability condition of low-density parity-check codes under both bitwise and blockwise maximum a posteriori decoding. As a consequence, we prove that the stability condition determines an upper bound on both the bitwise and the blockwise m ...
Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from error-correction performa ...
For the past 70 years or so, coding theorists have been aiming at designing transmission schemes with efficient encoding and decoding algorithms that achieve the capacity of various noisy channels. It was not until the '90s that graph-based codes, such as ...