How does Reed Solomon encoding work?

Reed Solomon codes are a subset of BCH codes and are linear block codes. A Reed-Solomon code is specified as RS(n,k) with s-bit symbols. This means that the encoder takes k data symbols of s bits each and adds parity symbols to make an n symbol codeword. There are n-k parity symbols of s bits each.

How many bits can Reed Solomon correct?

16
The standard (255, 223) Reed-Solomon code is capable of correcting up to 16 Reed-Solomon symbol errors in each codeword. Since each symbol is actually eight bits, this means that the code can correct up to 16 short bursts of error due to the inner convolutional decoder.

How the RS code is represented?

The main parameters of RS code are (n,k,δ), where n is the code length, k is the number of information symbols and δ stands for the minimum Hamming distance of the code. For a given redundancy, RS codes offer the largest δ since RS codes are maximum distance separable codes (MDS).

Is Reed Solomon a perfect code?

The Reed–Solomon code is optimal in the sense that the minimum distance has the maximum value possible for a linear code of size (n, k); this is known as the Singleton bound. Such a code is also called a maximum distance separable (MDS) code.

What is maximum distance separable code?

A maximum distance separable code (MDS code) is a code C for which |C| = |A|n-d+1. Thus, C has the property that for any k-tuple (k = n – d + 1) of elements of A on any k coordinates, there is a unique codeword of C which agrees with the k-tuple on these k coordinates.

Which algorithm is used in Viterbi decoder?

A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm).

What is Viterbi decoding algorithm?

The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding. It is most often used for decoding convolutional codes with constraint lengths k≤3, but values up to k=15 are used in practice. Viterbi decoding was developed by Andrew J.

Can we implement a Reed-Solomon encoder using the architecture?

It can be demonstrated that we can implement a Reed-Solomon encoder using the architecture of Figure 2 Since the Reed-Solomon is a Block Coding algorithm is clear from Figure 2 that during the coded symbols computation the algorithm pass through the input to the output ( sel =1).

What is an intuitive explanation of the QR Reed Solomon coding scheme?

Reed Solomon Coding is a block coding scheme it takes a block of k symbols at a time and append 2t parity symbols. Following figure illustrates the scheme. Encoder considers the k symbol block as a polynomial, M(x); of degree k-1, and first symbol being the coefficient of the most significant term.

What is Reed-Solomon block coding?

Since the Reed-Solomon is a Block Coding algorithm is clear from Figure 2 that during the coded symbols computation the algorithm pass through the input to the output ( sel =1).

What is the clock frequency of the Reed-Solomon encoder Rs on cyclone IV?

In FIGURE is reported an example of a layout on Cyclone IV Altera/Intel FPGA. As clear from the report in Figure 5 the Reed-Solomon encoder RS (7,3) takes only 37 logic element and 34 registers. The timing analysis reports a 474 MHz as the clock frequency.