Fixed errors correcting codes 400m 128 x 18August 12, 2020 by Anthony Middleton
In this tutorial, we will find out some of the possible causes that could lead to a 400m 128x18 error fix code and then give you possible solutions to this problem.
In computer science, telecommunications, information theory, and coding theory, an error correcting code, sometimes an error correcting code (ECC), is used to check for data errors in data links. unreliable or noisy communication.
In computer science, telecommunications, information theory, and coding theory, an error correcting code, sometimes an error correcting code (ECC), is used to check for data errors in data links. unreliable or noisy communication.   The basic idea is that the sender encodes the message with redundant information in ECC form. Redundancy allows the recipient to recognize a limited number of errors that can occur anywhere in the message and to correct those errors often without retransmission. American mathematician Richard Hamming was a pioneer in this field in the 1940s and invented the first error-correcting code in 1950: the Hamming code (7.4). Unlike error detection,
ECC is that errors that occur can be corrected and not easily identified. The advantage is that a system using ECC does not need a back channel to request retransmission of data when an error occurs. The disadvantage is that a fixed overhead is added to the message, which requires a higherdirect channel bandwidth. Therefore, ECC is used in situations where retransmissions are expensive or impossible, such as B. one-way links and when sending to multiple multicast recipients. Long latency connections also benefit. For a satellite orbiting Uranus, retransmission due to errors can cause a delay of five hours. ECC information is usually added to storage devices to enable recovery of damaged data. They are widely used in modems and are used in systems where the main memory is ECC memory.Receiver ECC processing can be applied to a digital bitstream or digitally modulated carrier demodulation. For the latter, ECC is an integral part of the original A / D conversion of the receiver. The Viterbi decoder implements a flexible decision-making algorithm for demodulating digital data from a noise-distorted analog signal. Many ECC encoders / decoders can also generate a BER (Bit Error Rate) signal that can be used as aProvides feedback for fine tuning the analog receiver electronics.
The maximum percentage of errors or missing bits that can be corrected is determined by the design of the ECC code, so different error correction codes are suitable for different conditions. Typically, a stronger code results in more redundancy to be transmitted using the available bandwidth, which lowers the effective bit rate and improves the effective received signal-to-noise ratio. The Shannon Code Noise Channel Coding Theorem answers the question of how much bandwidth is left for data transmission when using the most efficient code that sets the decoding error probability to zero. This sets limits on the theoretical maximum bit rate of channel information with a specific noise level. However, the evidence is not constructive and therefore does not provide information on how to build the ability to achieve code. After many years of research, some modernThese ECC systems today are [when?] very close to their theoretical maximum.
How It Works?
ECC is achieved by adding redundancy to the information transmitted using the algorithm. The redundant bit can be a complex function of many of the original bits of information. The original information may or may not appear literally in the encoded output. Codes that contain input data without changes in the output are systematic, but codes that do not contain are not.
A simplified example of ECC is to transmit each bit of data three times, which is called a repetition code (3.1). The receiver can see 8 versions of the output through a noisy channel, see the table below.
This fixes a bug in one of the three samples by "majority vote" or "democratic vote". The ability to correct this ECC:
While this modular triple redundancy is easy to implement and widely used, it is a relatively inefficient ECC. The best ECC codes usually look at the last dozen or even the last hundred bits previously received to determine how it should decode.There is a current small handful of bits (usually in groups of 2 to 8 bits).
Medium Noise To Reduce Errors 
We can say that ECC works by "noise averaging". Since each bit of data affects many transmitted symbols, noise corruption of some symbols usually extracts the original user data from other unmodified received symbols, which also depend on the same user data.
Most telecommunications systems use a fixed channel code that allows for the worst expected bit error rate and will not work at all if the bit error rate degrades. However, some systems adapt to these channel error conditions: in some cases of requesting an automatic restart, a fixed ECC method is used if the ECC can handle the error rate, and then switch to ARQ if the error rate becomes too high. Adaptive modulation and coding use different ECC rates, with more bits added for each packet to correcterror removal if there are higher error rates in the channel, or removed if not required,
ECC Types 
There are many types of block codes. Reed-Solomon encoding is widely used on CDs, DVDs, and hard drives. Other examples of classic block codes include Golay, BCH, Multidimensional Parity, and Hamming codes.
Hamming ECC is commonly used to fix NAND flash errors.  This provides one-bit error correction and 2-bit error detection. Hamming codes are only suitable for more reliable single cell NAND (SLC). Denser Multi-Level NAND Cell (MLC) can use a multi-bit ECC patch like BCH or Reed-Solomon.   NOR Flash is not usually used for bug fixing. 
Classical block codes are usually decoded using hard decision algorithms,  , which means that for each input signal, a hard decision is made and output, whether it is on or corresponds to a zero bit. In contrast, convolutional codes are usually decoded with anusing soft decision algorithms such as Viterbi, MAP or BCJR, which process analog (sampled) signals and provide much better error correction efficiency than a complex decoding solution.
Almost all classical block codes apply the algebraic properties of finite fields. Therefore, classical block codes are often called algebraic codes.
Unlike conventional block codes, which often indicate the ability to detect or correct errors, many modern block codes, such as LDPC codes, do not have such guarantees. Instead, modern codes are estimated by their bit error rate.
Most forward error correction codes only correct bit rollovers, not bit insertions or deletions. In this parameter, Hamming distance is a suitable way to measure the bit error rate. Some forward error correction codes are used to correct bit insertions and deletions, such as B. Marking codes and watermarks. Levenshtein distanceis a more suitable way to measure the bit error rate when using such codes. 
Code Speed And Trade-off Between Reliability And Baud Rate 
The basic principle of ECC is to add redundant bits to help the decoder find the real message encoded by the sender. The code rate of a given ECC system is defined as the ratio of the number of information bits to the total number of bits (i.e. information plus redundancy bits) in a communication packet. given. Therefore, the code rate is a real number. A low code rate close to zero implies a strong code that uses many redundant bits to operate normally, while a high code rate close to 1 implies a weak code.
Redundant bits that protect information must be sent with the same communication resources they want to protect. This leads to a fundamental tradeoff between reliability and throughput.  As a last resort, strong code (with low code rate) can cause a significant increase in the SNR of the receiver (signal-to-noise ratio) (reducing the bit error rate to at the expense of the effective data rate. On the other hand, without using ECC (i.e. code rate equal to 1), use the entire channel for transmission purposes information to the detriment of leaving bits without additional protection.
An interesting question: how effective can ECC be with a low decoding error rate in terms of information transfer? This question was answered by Claude Shannon in the second sentence, which states that channel bandwidth is the maximum bit rate that any ECC with an error rate close to zero can achieve:  His proof is based on random Gaussian coding, which is not suitable for real-world applications. Shannon's ceiling
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