Abstract:
A system, method and apparatus for encoding and decoding data in a distributed data storage and retrieval system. Data destined for storage is converted into information vectors, and the information vectors are multiplied by a binary encoder matrix to form systematic codewords. The binary encoder matrix is formed as a binary representation of an encoding matrix, the encoding matrix comprising an identity matrix and a special Cauchy matrix, where each element in encoding matrix is an element of an extension field.
Abstract:
According to some embodiments, a method for use in a wireless transmitter of a wireless communication network comprises encoding information bits using a parity check matrix (PCM) and transmitting the encoded information bits to a wireless receiver. The parity check matrix (PCM) is optimized according to two or more approximate cycle extrinsic message degree (ACE) constraints. In some embodiments, a first portion of the PCM is optimized according to a first ACE constraint and a second portion of the PCM is optimized according to a second ACE constraint.
Abstract:
An error correction and fault tolerance method and system for an array of disks is presented. The array comprises k + 5 disks, where k disks store user data and 5 disks store computed parity. The present invention further comprises a method and a system for reconstituting the original content of each of the k + 5 disks, when up to 5 disks have been lost, wherein the number of disks at unknown locations is E and the number of disks wherein the location of the disks is known is Z. All combinations of faulty disks wherein Z + 2 x E ≤ 4 are reconstituted. Some combinations of faulty disks wherein Z + 2 x E ≥-5 are either reconstituted, or errors are limited to a small list.
Abstract:
La présente invention concerne un codeur et un décodeur de code LDPC (Contrôle de Parité de Basse Densité) quasi-régulier admettant une matrice de contrôle représentée par un graphe bipartite de Tanner comprenant (128) noeuds variables du graphe et (64) noeuds de contraintes du graphe, basé sur un protographe comprenant (8) noeuds de variables et (4) noeuds de contraintes, chacun des noeuds contraintes du graphe étant connecté à (7) noeuds variables du graphe, chacun des noeuds de variables du graphe étant connecté à (3) ou (4) noeuds de contraintes du graphe, chacun des cycles du graphe ayant une longueur supérieure ou égale à 6, et la distance minimale dudit code étant égale ou supérieure à (14).
Abstract:
A method for quasi-cyclic low-density parity-check (QC-LDPC) encoding and decoding of a data packet by a lifted matrix is provided, the method comprising: lifting the QC-LDPC code for maximal code length Nmax and maximal circulant size Z upper of the base matrix; generating a plurality of optimal values r, for a plurality of circulants Z 1 , Z 2 ,...., Z upper based on the QC-LDPC code lifted for maximal length N max , 0 ≤ r; ≤ Z upper - 1; saving the generated plurality of optimal values r; corresponding to the plurality of circulants Z,, Z 2 ,..., Z upper and a matrix for the QC-LDPC code lifted for maximal length N max in the memory unit; receiving a current circulant Z current from the plurality of circulants Z 1 , Z 2 ,...., Z upper ; selecting a current optimal value r current from the plurality of optimal values r; stored in the memory unit corresponding to the current circulant Z current ; and lifting the base matrix based on the current optimal value r current , wherein a floor scale modular lifting of the base matrix is calculated as: where E(H upper ) is a value of circulant shift in the base matrix for maximal circulant size; wherein 0 ≤ r current ≤ z upper 1 and r current =1 is excluded. The apparatus for QC-LDPC encoding and decoding of a data packet by a lifted matrix is further provided.
Abstract:
A distributed storage system can use a high rate MSR erasure code to repair multiple nodes when multiple node failures occur. An encoder constructs m r-ary trees to determine the symbol arrays for the parity nodes. These symbol arrays are used to generate the parity data according to parity definitions or parity equations. The m r-ary trees are also used to identify a set of recovery rows across helper nodes for repairing a systematic node. When failed systematic nodes correspond to different ones of the m r-ary trees, a decoder may select additional recovery rows. The decoder selects additional recovery rows when the parity definitions do not provide a sufficient number of independent linear equations to solve the unknown symbols of the failed nodes. The decoder can select recovery rows contiguous to the already identified recovery rows for access efficiency.
Abstract:
A method and software product display errors of a tracking system that utilizes a plurality of receivers positioned around a tracking area to receive pings periodically transmitted by a tracking tag within the tracking area. For each locate received from the tracking system, a symbol indicative of the locate is plotted on a display graphically depicting the tracking area. A vector connecting each pair of chronologically consecutive symbols is plotted on the display, the vector visually indicating an error within the locates that would otherwise not be visible on the display. Another method concurrently displays predicted sensitivity for each of at least two receivers of a tracking system that locates tracking tags within a tracking area, the receivers being positioned within a surrounding area of the tracking area. A graphical representation of the surrounding area, the tracking area, and receiver sensitivities indicate the predicted receiver coverage of the tracking area.
Abstract:
Systems and methods of precoded faster than Nyquist (FTN) signalling are provided. In the transmitter, Tomlinson-Harashima Precoding (THP) is applied to produce precoded symbols. The THP is based on inter-symbol interference (ISI) due to using faster than Nyquist (FTN) signalling. An inverse modulo operation is not performed in the receiver. Instead, in the receiver, FTN processing is performed based on a matched filter output by determining log a-posteriori probability ratio LAPPR values computed for an n th bit bn of a k th received symbol and pre-computed a-priori probabilities of an extended constellation for a given pulse shape h(t) and FTN acceleration factor combination.
Abstract:
Apparatus, systems and methods for error detection in transmissions on a multi-wire interface are disclosed. A method for transmitting data on the multi-wire interface includes transmitting data on a multi-wire interface includes obtaining a plurality of bits to be transmitted over a plurality of connectors, converting the plurality of bits into a sequence of symbols, and transmitting the sequence of symbols on the plurality of connectors. A predetermined number of least significant bits in the plurality of bits may be used for error detection. The predetermined number of least significant bits may have a constant value that is different from each of a plurality of error values. A symbol error affecting one or two symbols in the sequence of symbols may cause a decoded version of the predetermined number of least significant bits to have value that is one of a plurality of error values.
Abstract:
A code book is generated for mapping source to target code words which allows encoding source data at reduced probability of incorrect decoding, e.g. for DNA storage. The target code words are grouped (102) into subsets and comprise identifying and remaining portions. The identifying portions of target code words corresponding to a same subset are identical. A first code symbol set of source code words is selected (103) for addressing the subsets. For the subsets,neighboring subsets are determined (104). The identifying portions of the target code words of neighboring subsets differ from those of the corresponding subset by up to a predetermined amount of symbols. Source code words are assigned (105) where the corresponding first code symbols address the same subset to said subset such that an amount of target code words of said subset having their remaining portions identical to their neighboring subsets corresponds to an optimization criterion.