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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.
A delta can be defined in 2 ways, symmetric delta and directed delta.A symmetric delta can be expressed as (,) = (),where and represent two versions.. A directed delta, also called a change, is a sequence of (elementary) change operations which, when applied to one version , yields another version (note the correspondence to transaction logs in databases).
Error-correcting codes are usually distinguished between convolutional codes and block codes: Convolutional codes are processed on a bit-by-bit basis. They are particularly suitable for implementation in hardware, and the Viterbi decoder allows optimal decoding. Block codes are processed on a block-by-block basis.
Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).
Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
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A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
hardware invesion of a finite field binary polynomial based number using a sub-field. - For example, an 8 bit field is normally implemented as finite field math modulo some 9 bit primitive polynomial. A compatable 8 bit field can also be implemented as finite field math modulo a 3 nibble (4 bit) polynomial 1 x 2 + a x + b. The coefficients of ...