Acyclic Tanner Graphs and Maximum-Likelihood Decoding of Linear Block Codes
نویسنده
چکیده
The maximum-likelihood decoding of linear block codes by the Wagner rule decoding is discussed. In this approach, the Wagner rule decoding which has been primarily applied to single parity check codes is employed on acyclic Tanner graphs. Accordingly, a coset decoding equipped with the Wagner rule decoding is applied to the decoding of a code C having a Tanner graph with cycles. A subcode C1 of C with acyclic Tanner graph is chosen as the base subcode. All cosets of C1 have the same Tanner graph and are distinguished by their values of parity nodes in the graph. The acyclic Tanner graph of C1 together with a trellis representation of the space of the parity sequences represent the code C. E cient use of this graphical presentation provides a uni ed and systematic approach to several ever best known maximum-likelihood decoding techniques of linear block codes. The hexacode H6, ternary Golay code G12, ReedMuller codes, Hamming codes, and the extended quadratic residue codes are discussed.
منابع مشابه
Which codes have cycle-free Tanner graphs?
If a linear block code C of length n has a Tanner graph without cycles, then maximum-likelihood soft-decision decoding of C can be achieved in time O(n). However, we show that cycle-free Tanner graphs cannot support good codes. Specifically, let C be an (n, k, d) linear code of rate R = k/n that can be represented by a Tanner graph without cycles. We prove that if R ≥ 0.5 then d ≤ 2, while if R...
متن کاملWhich Codes Have Cycle-free
If a linear block code C of length n has a Tanner graph without cycles, then maximum-likelihood soft-decision decoding of C can be achieved in time O(n 2). However, we show that cycle-free Tanner graphs cannot support good codes. Specically, let C be an (n;k;d) linear code of rate R = k=n that can be represented by a Tanner graph without cycles. We prove that if R 0:5 then d 2, while if R < 0:5...
متن کاملHierarchies of Local-Optimality Characterizations in Decoding of Tanner Codes
Recent developments in decoding of Tanner codes with maximum-likelihood certificates are based on a sufficient condition called local-optimality. We define hierarchies of locally-optimal codewords with respect to two parameters. One parameter is related to the minimum distance of the local codes in Tanner codes. The second parameter is related to the finite number of iterations used in iterativ...
متن کاملLocal-Optimality Characterizations in Decoding Tanner Codes
Recent developments in decoding Tanner codes with maximum-likelihood certificates are based on a sufficient condition called local-optimality. We define hierarchies of locally optimal codewords with respect to two parameters. One parameter is related to the distance of the local codes in Tanner codes. The second parameter is related to the finite number of iterations used in iterative decoding....
متن کاملPseudocodeword-Free Criterion for Codes with Cycle-Free Tanner Graph
Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cyclefree. Therefore, cycles are usually seen as the culprit of low-density parity-check (LDPC) codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effe...
متن کامل