Publication

Symbol-Pair Codes: Algebraic Constructions and Asymptotic Bounds

2011
Conference Papers

Abstract

For the recently proposed model of symbol-pair channels, we advance the pair-error coding theory with algebraic cyclic-code constructions and asymptotic bounds on code rates. Cyclic codes for pair-errors are constructed by a careful use of duals of known tools from cyclic-code theory. Asymptotic lower bounds on code rates show that codes for pair-errors provably exist for rates strictly higher than codes for the Hamming metric.

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2011
Conference Papers

Abstract

Official source

Related concepts (32)

Cyclic code

In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. Let be a linear code over a finite field (also called Galois field) of block length . is called a cyclic code if, for every codeword from , the word in obtained by a cyclic right shift of components is again a codeword.

Low-density parity-check code

In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed using a sparse Tanner graph (subclass of the bipartite graph). LDPC codes are , which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical maximum (the Shannon limit) for a symmetric memoryless channel.

Code rate

In telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant). That is, if the code rate is for every k bits of useful information, the coder generates a total of n bits of data, of which are redundant. If R is the gross bit rate or data signalling rate (inclusive of redundant error coding), the net bit rate (the useful bit rate exclusive of error correction codes) is .

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