3 research outputs found
Effects of Single-Cycle Structure on Iterative Decoding for Low-Density Parity-Check Codes
We consider communication over the binary erasure channel (BEC) using
low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For
fixed numbers of BP iterations, the bit error probability approaches a limit as
blocklength tends to infinity, and the limit is obtained via density evolution.
On the other hand, the difference between the bit error probability of codes
with blocklength and that in the large blocklength limit is asymptotically
where denotes a
specific constant determined by the code ensemble considered, the number of
iterations, and the erasure probability of the BEC. In this paper,
we derive a set of recursive formulas which allows evaluation of the constant
for standard irregular ensembles. The dominant difference
can be considered as effects of cycle-free and
single-cycle structures of local graphs. Furthermore, it is confirmed via
numerical simulations that estimation of the bit error probability using
is accurate even for small blocklengths.Comment: 16 pages, 7 figures, submitted to IEEE Transactions on Information
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