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The advantage of choosing a primitive polynomial as the generator for a CRC code is that the resulting code has maximal total block length in the sense that all 1-bit errors within that block length have different remainders (also called syndromes) and therefore, since the remainder is a linear function of the block, the code can detect all 2 ...
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.
The W3C webpage on PNG includes an appendix with a short and simple table-driven implementation in C of CRC-32. [4] You will note that the code corresponds to the lsbit-first byte-at-a-time pseudocode presented here, and the table is generated using the bit-at-a-time code. Using a 256-entry table is usually most convenient, but other sizes can ...
The cyclic redundancy check (CRC) is based on division in the ring of polynomials over the finite field GF (2) (the integers modulo 2 ), that is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around. Any string of bits can be interpreted as the coefficients of a message polynomial of this ...
Since most such codes correct only bit-flips, but not bit-insertions or bit-deletions, the Hamming distance metric is the appropriate way to measure the number of bit errors. Many FEC coders also continuously measure the current BER.
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.
The default OperandSize and AddressSize to use for each instruction is given by the D bit of the segment descriptor of the current code segment - D=0 makes both 16-bit, D=1 makes both 32-bit. Additionally, they can be overridden on a per-instruction basis with two new instruction prefixes that were introduced in the 80386:
The 64-bit timestamps used by NTP consist of a 32-bit part for seconds and a 32-bit part for fractional second, giving NTP a time scale that rolls over every 2 32 seconds (136 years) and a theoretical resolution of 2 −32 second (233 picoseconds). NTP uses an epoch of 1 January 1900.