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Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably transmitted over a communication channel.
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 complete block has m + n bits of data with a code rate of m/(m + n). The permutation of the payload data is carried out by a device called an interleaver . Hardware-wise, this turbo code encoder consists of two identical RSC coders, C 1 and C 2 , as depicted in the figure, which are connected to each other using a concatenation scheme ...
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.
What is the channel capacity for a signal having a 1 MHz bandwidth, received with a SNR of −30 dB ? That means a signal deeply buried in noise. −30 dB means a S/N = 10 −3. It leads to a maximal rate of information of 10 6 log 2 (1 + 10 −3) = 1443 bit/s. These values are typical of the received ranging signals of the GPS, where the ...
Shannon's main result, the noisy-channel coding theorem, showed that, in the limit of many channel uses, the rate of information that is asymptotically achievable is equal to the channel capacity, a quantity dependent merely on the statistics of the channel over which the messages are sent.
The converse of the capacity theorem essentially states that () is the best rate one can achieve over a binary symmetric channel. Formally the theorem states: Formally the theorem states:
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...