Beyond the Bethe Free Energy of LDPC Codes via Polymer Expansions
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We consider discrete message passing (MP) decoding of low-density parity check (LDPC) codes based on information-optimal symmetric look-up table (LUT). A link between discrete message labels and the associated log-likelihood ratio values (defined in terms ...
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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 ...
Polar codes are a new class of block codes with an explicit construction that provably achieve the capacity of various communications channels, even with the low-complexity successive-cancellation (SC) decoding algorithm. Yet, the more complex successive-c ...
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 ...
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 ...
The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy associated with a l ...
The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding ...