Graph theory and its applications
Graph theory and its applications
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
Modern Coding Theory
Which codes have cycle-free Tanner graphs?
IEEE Transactions on Information Theory
Upper bounds on the rate of LDPC codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Parity-Check Density Versus Performance of Binary Linear Block Codes: New Bounds and Applications
IEEE Transactions on Information Theory
Extremal Problems of Information Combining
IEEE Transactions on Information Theory
The renaissance of Gallager's low-density parity-check codes
IEEE Communications Magazine
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This work introduces an information-theoretic lower bound on the number of fundamental cycles for bipartite graphs of low-density parity-check (LDPC) code ensembles. This information-theoretic bound is expressed in terms of the achievable gap to capacity when the transmission of the code ensemble takes place over a memoryless binary-input output-symmetric (MBIOS) channel. The bound shows quantitatively the necessity of cycles in bipartite graphs which represent good LDPC code ensembles. More explicitly, it shows that the number of fundamental cycles should grow at least like log 1/Ɛ where Ɛ designates the gap in rate to capacity, hence, it is unbounded as the gap to capacity vanishes. For the derivation of this bound, a new information-theoretic lower bound on the average right degree, which also behaves like log 1/Ɛ, is derived. The interested reader is referred to the full paper version [9].