Title :
Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes
Author :
Miller, Gadi ; Burshtein, David
Author_Institution :
Dept. of Electr. Eng. Syst., Tel Aviv Univ., Israel
fDate :
11/1/2001 12:00:00 AM
Abstract :
We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent
Keywords :
channel capacity; error detection codes; error statistics; linear codes; maximum likelihood decoding; memoryless systems; Gallager´s bound; LDPC codes; average spectrum; binary-input symmetric-output channel; channel capacity; discrete memoryless channel; ensemble averaged decoding error probability; error exponent; linear codes; low-density parity-check codes; lower bounds; maximum-likelihood decoding error probability; random coding exponent; reliable communication; upper bounds; Channel capacity; Code standards; Error probability; Iterative algorithms; Iterative decoding; Maximum likelihood decoding; Parity check codes; Polynomials; Turbo codes; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on