Sideband Boundary Asymmetry Scan

Sideband Boundary Asymmetry Three-Row Scan

A red sideband has a real floor at packet zero; a blue sideband has no matching ceiling in this model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Red sideband has a real floor at packet zero

Chapter two already established that a red sideband at packet index zero is rejected -- there is no packet below zero to drop into, so the accepted bit reads 0.

ni=0,nf=0,a=0n_i=0,\quad n_f=0,\quad a=0
Red sideband at the floorThe rejected row sits exactly at the packet-zero floor.driveEnergy=6 JstartPacket=0 packetendPacket=0 packetmatchedBit=1 bitacceptedBit=0 bit

Blue sidebands never hit an equivalent ceiling in this model

One packet above the floor, red is accepted normally. Chapter five's blue-growth scan only ever checked small starting packets, up through two. Scanning a blue sideband from a much higher starting packet shows this toy model enforces a floor for red but never enforces any matching ceiling for blue.

kindninfared000red101blue20211\begin{array}{c|c|c|c}\text{kind}&n_i&n_f&a\\\text{red}&0&0&0\\\text{red}&1&0&1\\\text{blue}&20&21&1\\\end{array}
Red sideband above the floorOne packet above zero, the same red drive is accepted.driveEnergy=6 JstartPacket=1 packetendPacket=0 packetmatchedBit=1 bitacceptedBit=1 bit

A high-packet blue sideband is still accepted without limit

Starting from packet 20, the blue sideband still adds one packet and is still accepted. Nothing in this model's blue-sideband rule checks for an upper packet limit the way the red rule checks for the zero floor.

ni=20,nf=21,a=1n_i=20,\quad n_f=21,\quad a=1
High-packet blue sidebandThe final row is rendered as the checked high-packet case.driveEnergy=10 JstartPacket=20 packetendPacket=21 packetmatchedBit=1 bitacceptedBit=1 bit