Bounded LFSR for Row Hammer Mitigation
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Solution Overview
Problem
Conventional linear-feedback shift registers (LFSRs) generate pseudorandom numbers that eventually repeat, causing issues when certain values within the maximum-length sequence are undesirable, particularly in applications like memory devices where timing constraints are critical, such as row hammer mitigation.
Innovation Solution
A bounded LFSR is designed to produce a shorter sequence with a maximum value less than that of a conventional LFSR, comprising an upper and lower portion LFSR operating on the same clock signals, allowing for the generation of random numbers within a valid range by skipping specific values in the upper portion sequence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a conventional LFSR is used to generate pseudorandom numbers, then the sequence length is maximized (2^n - 1), but certain values within the sequence may be undesirable and timing constraints cannot be met
Solution Approach 1:
The LFSR is divided into two independent portions: a first LFSR that generates a sequence of values and a second LFSR that generates a modified sequence by skipping certain values. This segmentation allows each portion to operate independently with different sequence characteristics, enabling the system to meet both speed and validity requirements.
Solution Approach 2:
The patent changes the sequence generation parameters by introducing a skip mechanism in the second LFSR. Instead of generating all 2^n - 1 possible values, the second LFSR skips specific values (e.g., values greater than a threshold or specific patterns), effectively changing the output distribution to meet validity constraints while maintaining generation speed.
2Adaptability or versatility
If a conventional LFSR generates the maximum-length sequence, then the sequence covers the full range of possible values, but the maximum value may exceed the valid range for consuming circuits
Solution Approach 1:
The second LFSR extracts only the desirable values from the full sequence generated by the first LFSR. By implementing a skip mechanism that removes unwanted values (e.g., values exceeding a maximum threshold), the system extracts a subset of valid values that meet the requirements of consuming circuits while maintaining the pseudorandom characteristics.
3Reliability
If the LFSR sequence is extended to maximize randomness, then the period increases, but the time to generate a valid random number increases
Solution Approach 1:
The second LFSR performs preliminary filtering of the sequence in advance by pre-configuring the skip mechanism. Instead of generating the full maximum-length sequence and then filtering it, the system pre-establishes which values to skip, allowing valid random numbers to be generated more quickly without sacrificing randomness quality.
Data Source
AI summary
Linear-feedback shift registers (LFSRs) for generating bounded random numbers (e.g., random numbers within a narrower range than those generated by a conventional LFSR of the same width) are described. In one embodiment, a bounded LFSR for generating an n-bit value comprises an m-bit LFSR with a range of 2m random numbers and an n−m bit LFSR with a range of 2n-m−1−k random numbers. The bounded LFSR further comprises logic to skip k values from a repeatable sequence of the n−m bit LFSR, which can, for example, be configured during the design of the bounded LFSR. The bounded LFSR provides bounded random numbers based on the outputs of the m-bit LFSR and the n−m bit LFSR. In one embodiment, the bounded random number generated by the bounded LFSR is used as a random address in a row hammer mitigation system.