## How do you use the Reed-Solomon code?

Decoding using Reed Solomon Code

- The receiver receives the message r(x) and divides it by the generator polynomial g(x).
- If r(x)/g(x)=0, then it implies no error.
- If r(x)/g(x)≠0, then the error polynomial is evaluated using the expression: r(x) = p(x) * g(x) + e(x)
- The error polynomial gives the error positions.

**How do you make a Reed-Solomon code?**

These symbols can be used to construct a polynomial P(x) = mo + m00-\ \-mk~2Xk~2 + nik-]Xk~l. A Reed-Solomon code word c is formed by evaluating P(x) at each of the q elements in the finite field GF(g). A complete set of code words is constructed by allowing the k information symbols to take on all possible values.

### How many bits can Reed Solomon correct?

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.

**What is Reed-Solomon code describe its decoding process?**

The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block. More importantly, it flags as erasures any uncorrectable blocks, i.e., blocks with more than 2 byte errors.

## How many errors can Reed Solomon detect?

16 symbol errors

There are n-k parity symbols of s bits each. A Reed-Solomon decoder can correct up to t symbols that contain errors in a codeword, where 2t = n-k. The decoder can correct any 16 symbol errors in the code word: i.e. errors in up to 16 bytes anywhere in the codeword can be automatically corrected.

**How is coding gain calculated?**

Example. If the uncoded BPSK system in AWGN environment has a bit error rate (BER) of 10−2 at the SNR level 4 dB, and the corresponding coded (e.g., BCH) system has the same BER at an SNR of 2.5 dB, then we say the coding gain = 4 dB − 2.5 dB = 1.5 dB, due to the code used (in this case BCH).

### Who invented turbo codes?

Claude Berrou

Claude Berrou, Punya Thitimajshima, and Berrou’s late research partner Alain Glavieux invented turbo codes, thereby solving a data communications puzzle that had evaded researchers for 40 years.

**Are turbo codes block codes?**

Because turbo codes are linear block codes, the encoding operation can be viewed as the modulo-2 matrix multiplica- tion of an information vector with a generator matrix.

## Which code corrects the most errors?

Hamming code

The method of detecting and correcting burst errors in the data sequence is called “Burst error correction”. Hamming code or Hamming Distance Code is the best error correcting code we use in most of the communication network and digital systems.

**How is ECC calculated?**

The number of ECC bits for generation is dependent on size of the data & can be calculated using below formula : SECDED : 2^n+1: where n+1 = number of ECC bits. DECTED : 2^n+2: Where n+2 = number of ECC bits.