This contribution aims at unveiling the properties of the Tanner graphs underlying LDPC convolutional codes that can be used for efficient decoder implementations. We will also shown an implementation example of a simple programmable architecture that was obtained applying these graph properties.

The relation between the girth and the error correction capability of column-weight-three LDPC codes is investigated. Specifically, it is shown that the Gallager A algorithm can correct g/2 − 1 errors in g/2 iterations on a Tanner graph of girth g ≥ 10.

LDPC codes constructed from permutation matrices have recently attracted the interest of many researchers. A crucial point when dealing with such is trying to avoid cycles short length in associated Tanner graph, i.e. obtaining a possibly large girth. In this paper, we provide framework obtain constructions codes. We relate criteria for existence certain some number-theoretic concepts, particul...

We analyze the effect of redundant parity-check equations on the error-floor performance of low-density paritycheck (LDPC) codes used over the additive white Gaussian noise (AWGN) channel. Our findings show that a large number of iterative decoding errors in the [2640, 1320] Margulis code, confined to point trapping sets in the standard Tanner graph, can be corrected if only one redundant parit...

One of the phenomena that influences significantly the performance of low-density parity-check codes is known as trapping sets. An (a, b) elementary trapping set, or simply an ETS where a is the size and b is the number of degree-one check nodes and b a < 1, causes high decoding failure rate and exert a strong influence on the error floor. In this paper, we provide sufficient conditions for exp...

Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several intriguing problems in the intersection of coding theory and graph theory. In this paper, we study codes defined by planar Tanner graphs. We derive an upper bound on...

LDPC codes are serious contenders to Turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m ≥ 2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m, q) on 2qm vertices, which has girth at least 2dm/2e+ 4. We regard these graphs as Tanner graphs of binar...

A new class of error-correcting codes is created from a matrix operation defined within. The matrix operation takes a point-block incidence and produces a new point-block incidence with some desirable properties, including a doubling of the girth of the Tanner graph of the initial matrix. A specific example is created using PG(2, q), and the results are generalized to any point-block incidence ...

We introduce a group algebra formulation for bit optimal decoding of binary block codes. We use this new framework to give a simple algebraic proof that Pearl’s and Gallager’s belief propagation decoding algorithms are bit-optimal when the Tanner graph of the code is a tree. We believe that these derivations of known results give new insights into the issues of decoding on graphs from the algeb...