Inversion encoding

Inversion Encoding is an encoding technique used for encoding bus transmissions for low power systems. It is based on the fact that a large amount of power is wasted because of transitions, and thus reducing the transitions will help in power optimizations. This is done introducing an additional line named INV to the bus lines. This line determines whether the lines should be inverted or not.

Overview

The Bus-Invert encoding technique uses an extra signal (INV) to indicate the “polarity” of the data. Let the Bus-Invert code word be denoted as INV@x where @ is the concatenation operator, and x denotes either the source word or its one’s complement. The Bus-Invert decoder takes the code word and produces the corresponding source word as follows: If the INV signal is set, the result is one’s complement of x; otherwise it is x.

Usage Situations

• High capacitance lines
• High switching activities

Bus-Invert method

1. Compute the Hamming Distance (the number of bits in which they differ) between the present bus value (also counting the present invert line) and the next data value.
2. If the Hamming distance is larger than n/2, set invert = 1, and make the next bus value equal to the inverted next data value.
3. Otherwise let invert = 0, and let the next bus value equal to the next data value.
4. At the receiver side the contents of the bus must be conditionally inverted according to the invert line, unless the data is not stored encoded as it is (e.g., in a RAM). In any case, the vaue of invert must be transmitted over the bus (the method increases the number of line from n to n+1).

Example

Let us consider an example of a system which gets one of its data from a sensor. Most of the times, the sensor may be measuring some noise and for this example, let us consider that the values being measured are (0) and (-1) alternatively. For a 32-bit data bus, value 0 translates to 0x00000000 (0000 0000 0000 0000 0000 0000 0000 0000) while (-1) translates to 0xFFFFFFFF (1111 1111 1111 1111 1111 1111 1111 1111) in a 2’s complement representation. We see that the hamming distance in this case is 32 (since all 32-bits are changing their state). Using the signed bit representation, the hamming distance is significantly minimized. However, even using 2’s complement, we can achieve the same activity reduction using inversion encoding. So, 0 will be represented as 0x00000000 with INV=0 and -1 will be represented as 0x00000000 with INV=1. Since INV=1, receiver will invert the data before consuming it, thereby converting it to 0xFFFFFFFF internally. In this case, only 1 bit (INV bit) is changed over bus leading to an activity of factor 1, which is even better than signed bit representation.

Overview for Performance Analysis: inversion encoding

Performance Analysis

The Bus-Invert method generates a code that has the property that the maximum number of transitions per time-slot is reduced from n to n/2 and thus the peak power dissipation for I/O is reduced by half. From the coding theory point of view, the Bus-Invert code is a time-dependent Markovian code.

While the maximum numHamming distanceber of transitions is reduced by half, the average number of transitions is not that good. For an 8-bit bus for example, the average number of transitions, using bus-invert coding becomes 3.27 (instead of 4), or 0.41 (instead of 0.5) transitions per bus-line per time-slot. This means that the average number of transitions is 81.8% as compared with an unencoded bus. There are two reasons why the performance of the Bus-Invert coding for decreasing the average number of transitions is not as good as for decreasing the maximum number of transitions:

• The invert line contributes itself with some transitions.
• The distribution of the Hamming distances for the next data values is not uniform.

Partitioned Inversion Encoding

In order to decrease the average I/O power dissipation for wide buses the observation that the Bus-Invert method performs better for small n can be used to partition the bus into several narrower subbuses. Each of these subbuses can then be coded independently with its own invert signal. For example a 64-bit bus could be partitioned into eight 8-bit subbuses with a total of eight n order to decrease the average I/O power dissipation for wide buses the observation that the Bus-Invert method performs better for small n can be used to partition the bus into several narrower subbuses. Each of these subbuses can then be coded independently with its own invert signal. For example a 64-bit bus could be partitioned into eight 8-bit subbuses with a total of eight invert signals. Because of the assumption that the data to be transferred over the wide bus is random uniformly distributed, the statistics for the narrower subbuses will be independent and the sequence of data for each subbus will be random uniformly distributed. For example for a 64-bit bus partitioned into eight 8-bit subbuses the average number of transitions per time-slot will be 26.16 (8 times 3.27, the average for one 8-bit subbus) and the average number of transitions per bus-line per time-slot will be .41 (as for an 8-bit bus with one invert line). The maximum number of transitions is not improved by partitioning the bus and remains the same n/2. However, there is always an extra overhead of using more lines, but computationally, it has been found that the inversion bus encoding works well for most purposes.

See also

• Bus Encoding
• Two's Complement
• Low-power electronics
• Power Dissipation