1-of-N Coding System

A 1-of-N Coding System is a constant-weight coding that is a binary system.

Binary Gray code One-hot/1-of-N
000 000 00000001
001 001 00000010
010 011 00000100
011 010 00001000
100 110 00010000
101 111 00100000
110 101 01000000
111 100 10000000

References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/One-hot Retrieved:2015-2-18.
• In digital circuits, one-hot refers to a group of bits among which the legal combinations of values are only those with a single high (1) bit and all the others low (0).

A similar implementation in which all bits are '1' except one '0' is sometimes called one-cold.

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Constant-weight_code#1_of_N_codes Retrieved:2015-2-18.
• A special case of constant weight codes are the one-of-N codes, that encode $\displaystyle{ log_2 N }$ bits in a code-word of $\displaystyle{ N }$ bits. The one-of-two code uses the code words 01 and 10 to encode the bits '0' and '1'. A one-of-four code can use the words 0001, 0010, 0100, 1000 in order to encode two bits 00, 01, 10, and 11. An example is dual rail encoding, and chain link used in delay insensitive circuits. For these codes, $\displaystyle{ n=N,~ d=2,~ w=1 }$ and $\displaystyle{ A(n, d, w) = n }$.

Some of the more notable uses of one-hot codes include

﻿ ﻿biphase mark code uses a 1 of 2 code;

﻿ ﻿pulse-position modulation uses a 1 of n code;

• … Note that, in some fields, such as natural language processing, the categorical and multinomial distributions are conflated, and it is common to speak of a "multinomial distribution" when a categorical distribution is actually meant. This stems from the fact that it is sometimes convenient to express the outcome of a categorical distribution as a "1-of-K" vector (a vector with one element containing a 1 and all other elements containing a 0) rather than as an integer in the range $\displaystyle{ 1 \dots K }$; in this form, a categorical distribution is equivalent to a multinomial distribution over a single trial.