Performance analysis of linear codes under maximum-likelihood decoding: a tutorial
Communications and Information Theory
Bounds on the number of iterations for turbo-like ensembles over the binary erasure channel
IEEE Transactions on Information Theory
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
Modern Coding Theory
IEEE Transactions on Information Theory
Sphere-packing bounds revisited for moderate block lengths
IEEE Transactions on Information Theory
Capacity-achieving ensembles for the binary erasure channel with bounded complexity
IEEE Transactions on Information Theory
Parity-Check Density Versus Performance of Binary Linear Block Codes: New Bounds and Applications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
An Improved Sphere-Packing Bound for Finite-Length Codes Over Symmetric Memoryless Channels
IEEE Transactions on Information Theory
Capacity Achieving LDPC Codes Through Puncturing
IEEE Transactions on Information Theory
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This paper considers information-theoretic lower bounds on the graphical complexity of finite-length LDPC codes. It is assumed that the transmission of the codes takes place over a memoryless binary-input output-symmetric (MBIOS) channel, and the bounds are expressed as a function of the code performance and their achievable gap to capacity (either under ML decoding or any sub-optimal decoding algorithm). The lower bounds on the graphical complexity are compared to some explicit LDPC codes (or code ensembles), showing that these bounds are informative for considering the fundamental tradeoff which exists between the performance and graphical complexity of finite-length LDPC codes. This work relies on the full paper version [15].