Title :
Bounds on the Tradeoff Between Decoding Complexity and Rate for Sparse-Graph Codes
Author_Institution :
Univ. of California at Berkeley, Berkeley
Abstract :
Khandekar and McEliece suggested the problem of per bit decoding complexity for capacity achieving sparse-graph codes as a function of their gap from the channel capacity. We consider the problem for the case of the binary symmetric channel. We derive a lower bound on this complexity for some codes on graphs for Belief Propagation decoding. For bounded degree LDPC and LDGM codes, any concatenation of the two, and punctured bounded-degree LDPC codes, this reduces to a lower bound of O (log (1/isin-)). The proof of this result leads to an interesting necessary condition on the code structures which could achieve capacity with bounded decoding complexity over BSC: the average edge-degree must converge to infinity while the average node-degree must be bounded. That is, one of the node degree distributions must have a finite mean and an infinite variance.
Keywords :
channel capacity; computational complexity; decoding; graph theory; parity check codes; LDGM; LDPC; belief propagation decoding; binary symmetric channel; bounded decoding complexity; channel capacity; per bit decoding complexity; sparse-graph codes; Belief propagation; Capacity planning; Channel capacity; Circuits; Concatenated codes; H infinity control; Iterative decoding; Lakes; Parity check codes; Upper bound;
Conference_Titel :
Information Theory Workshop, 2007. ITW '07. IEEE
Conference_Location :
Tahoe City, CA
Print_ISBN :
1-4244-1564-0
Electronic_ISBN :
1-4244-1564-0
DOI :
10.1109/ITW.2007.4313073