Data processing: artificial intelligence – Neural network
Reexamination Certificate
2001-10-10
2003-10-14
Starks, Jr., Wilbert L. (Department: 2121)
Data processing: artificial intelligence
Neural network
C706S016000, C341S107000
Reexamination Certificate
active
06633856
ABSTRACT:
FIELD OF THE INVENTION
The present invention is directed to methods and apparatus for detecting and/or correcting errors in binary data, e.g., through the use of parity check codes such as low density parity check (LDPC) codes.
BACKGROUND
In the modern information age binary values, e.g., ones and zeros, are used to represent and communicate various types of information, e.g., video, audio, statistical information, etc. Unfortunately, during storage, transmission, and/or processing of binary data, errors may be unintentionally introduced, e.g., a one may be changed to a zero or vice versa.
Generally, in the case of data transmission, a receiver observes each received bit in the presence of noise or distortion and only an indication of the bit's value is obtained. Under these circumstances one interprets the observed values as a source of “soft” bits. A soft bit indicates a preferred estimate of the bit's value, i.e., a one or a zero, together with some indication of that estimate's reliability. While the number of errors may be relatively low, even a small number of errors or level of distortion can result in the data being unusable or, in the case of transmission errors, may necessitate re-transmission of the data.
In order to provide a mechanism to check for errors and, in some cases, to correct errors, binary data can be coded to introduce carefully designed redundancy. Coding of a unit of data produces what is commonly referred to as a codeword. Because of its redundancy, a codeword will often include more bits than the input unit of data from which the codeword was produced.
When signals arising from transmitted codewords are received or processed, the redundant information included in the codeword as observed in the signal can be used to identify and/or correct errors in or remove distortion from the received signal in order to recover the original data unit. Such error checking and/or correcting can be implemented as part of a decoding process. In the absence of errors, or in the case of correctable errors or distortion, decoding can be used to recover from the source data being processed, the original data unit that was encoded. In the case of unrecoverable errors, the decoding process may produce some indication that the original data cannot be fully recovered. Such indications of decoding failure can be used to initiate retransmission of the data.
While data redundancy can increase the reliability of the data to be stored or transmitted, it comes at the cost of storage space and/or the use of valuable communications bandwidth. Accordingly, it is desirable to add redundancy in an efficient manner, maximizing the amount of error correction/detection capacity gained for a given amount of redundancy introduced into the data.
With the increased use of fiber optic lines for data communication and increases in the rate at which data can be read from and stored to data storage devices, e.g., disk drives, tapes, etc., there is an increasing need not only for efficient use of data storage and transmission capacity but also for the ability to encode and decode data at high rates of speed.
While encoding efficiency and high data rates are important, for an encoding and/or decoding system to be practical for use in a wide range of devices, e.g., consumer devices, it is important that the encoders and/or decoders be capable of being implemented at reasonable cost. Accordingly, the ability to efficiently implement encoding/decoding schemes used for error correction and/or detection purposes, e.g., in terms of hardware costs, can be important.
Various types of coding schemes have been used over the years for error correction purposes. One class of codes, generally referred to as “turbo codes” were recently invented (1993). Turbo codes offer significant benefits over older coding techniques such as convolutional codes and have found numerous applications.
In conjunction with the advent of turbo codes, there has been increasing interest in another class of related, apparently simpler, codes commonly referred to as low density parity check (LDPC) codes. LDPC codes were actually invented by Gallager some 40 years ago (1961) but have only recently come to the fore. Turbo codes and LDPC codes are coding schemes that are used in the context of so-called iterative coding systems, that is, they are decoded using iterative decoders. Recently, it has been shown that LDPC codes can provide very good error detecting and correcting performance, surpassing or matching that of turbo codes for large codewords, e.g., codeword sizes exceeding approximately 1000 bits, given proper selection of LDPC coding parameters. Moreover, LDPC codes can potentially be decoded at much higher speeds than turbo codes.
In many coding schemes, longer codewords are often more resilient for purposes of error detection and correction due to the coding interaction over a larger number of bits. Thus, the use of long codewords can be beneficial in terms of increasing the ability to detect and correct errors. This is particularly true for turbo codes and LDPC codes. Thus, in many applications the use of long codewords, e.g., codewords exceeding a thousand bits in length, is desirable.
The main difficulty encountered in the adoption of LDPC coding and Turbo coding in the context of long codewords, where the use of such codes offers the most promise, is the complexity of implementing these coding systems. In a practical sense, complexity translates directly into cost of implementation. Both of these coding systems are significantly more complex than traditionally used coding systems such as convolutional codes and Reed-Solomon codes.
Complexity analysis of signal processing algorithms usually focuses on operations counts. When attempting to exploit hardware parallelism in iterative coding systems, especially in the case of LDPC codes, significant complexity arises not from computational requirements but rather from routing requirements. The root of the problem lies in the construction of the codes themselves.
LDPC codes and turbo codes rely on interleaving messages inside an iterative process. In order for the code to perform well, the interleaving must have good mixing properties. This necessitates the implementation of a complex interleaving process.
LDPC codes are well represented by bipartite graphs, often called Tanner graphs, in which one set of nodes, the variable nodes, corresponds to bits of the codeword and the other set of nodes, the constraint nodes, sometimes called check nodes, correspond to the set of parity-check constraints which define the code. Edges in the graph connect variable nodes to constraint nodes. A variable node and a constraint node are said to be neighbors if they are connected by an edge in the graph. For simplicity, we generally assume that a pair of nodes is connected by at most one edge. To each variable node is associated one bit of the codeword. In some cases some of these bits might be punctured or known, as discussed further below.
A bit sequence associated one-to-one with the variable node sequence is a codeword of the code if and only if, for each constraint node, the bits neighboring the constraint (via their association with variable nodes) sum to zero modulo two, i.e., they comprise an even number of ones.
The decoders and decoding algorithms used to decode LDPC codewords operate by exchanging messages within the graph along the edges and updating these messages by performing computations at the nodes based on the incoming messages. Such algorithms will be generally referred to as message passing algorithms. Each variable node in the graph is initially provided with a soft bit, termed a received value, that indicates an estimate of the associated bit's value as determined by observations from, e.g., the communications channel. Ideally, the estimates for separate bits are statistically independent. This ideal can be, and often is, violated in practice. A collection of received values constitutes a received word. For purposes of this application we may identify the
Novichkov Vladimir
Richardson Tom
Flarion Technologies, Inc.
Starks, Jr. Wilbert L.
Straub Michael P.
Straub & Pokotylo
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