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In fact, the term "list-decoding capacity" should actually be read as the capacity of an adversarial channel under list decoding. Also, the proof for list-decoding capacity is an important result that pin points the optimal trade-off between rate of a code and the fraction of errors that can be corrected under list decoding.
In coding theory, list decoding is an alternative to unique decoding of error-correcting codes in the presence of many errors. If a code has relative distance δ {\displaystyle \delta } , then it is possible in principle to recover an encoded message when up to δ / 2 {\displaystyle \delta /2} fraction of the codeword symbols are corrupted.
As with ideal observer decoding, a convention must be agreed to for non-unique decoding. The maximum likelihood decoding problem can also be modeled as an integer programming problem. [1] The maximum likelihood decoding algorithm is an instance of the "marginalize a product function" problem which is solved by applying the generalized ...
Based on their intended meanings and imagined decoding strategies, media producers execute certain encoding strategies and give a certain shape to the text. In the decoding process, viewers derive both perceived meanings and perceived encoding strategies from the text. From these two dimensions, viewers arrive at their evaluation of the text.
List decoding is useful when a codeword is corrupted in more than / places, where is the minimum Hamming distance between two codewords. In this case, it is no longer possible to identify exactly which original message has been encoded, since there could be multiple codewords within δ {\displaystyle \delta } distance of the corrupted codeword.
To convolutionally encode data, start with k memory registers, each holding one input bit.Unless otherwise specified, all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where the logic is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 0), and n generator polynomials — one for each adder (see figure below).
Various strategies can be applied such as chunking and mnemonics to aid in encoding, and in some cases, allow deep processing, and optimizing retrieval. Words studied in semantic or deep encoding conditions are better recalled as compared to both easy and hard groupings of nonsemantic or shallow encoding conditions with response time being the ...
Using list decoding, however, it is possible to compute a short list of possible candidate messages as long as fewer than of the bits in the received word have been corrupted. In code-division multiple access (CDMA) communication, the Hadamard code is referred to as Walsh Code, and is used to define individual communication channels .