Week 8 Workshop: Copying without loss

What resources can protect a message from a specified error pattern?

21 April 2027

What resources can protect a message from a specified error pattern?

Learning target. Calculate redundancy overhead and state the protection’s limit.

Before the workshop#

No pack to download. Every bitstring in this workshop is written on the page, and the only tool required is counting by hand.

The scheme. A 3x repetition code: to send one payload bit, send it three times. To decode a received triplet, take the majority value of its three bits. This scheme corrects any single bit-flip per triplet and no more — that bound is the whole week.

The worked message. Payload 1011 (4 bits). Encoded one bit at a time — 1→111, 0→000, 1→111, 1→111 — the transmitted codeword is 111 000 111 111 (12 bits).

Check — 5 minutes#

Received: 101 000 111 111. Decode each triplet by majority vote and write the recovered 4-bit payload. Then state, in one sentence, the assumption under which your decoded answer is reliable.

Receive — 15 minutes#

Confirm you can state, without looking back: what a triplet’s majority vote returns when it has zero errors, one error, and two errors — and which of those three cases the scheme’s guarantee actually covers.

Investigate — 40 minutes#

Decode a protected example (10 minutes). Received: 111 001 111 110. Decode each triplet by majority vote and write the recovered 4-bit payload. Two triplets here carry one flipped bit each; the other two have none — every triplet should still decode to the original payload.

Compare three parallel cases of the same single-bit corruption (15 minutes). The same physical fault — one bit flips in transit — is applied three ways to the same payload bit (1, sent as 111):

Write one sentence on what the failure row shows: the repetition code paid three times the bits and still failed exactly as silently as sending the bit unprotected once — because two flips inside one triplet is outside what a 3x repetition code was ever built to survive.

Calculate payload, transmitted bits and overhead (15 minutes). For a new 6-bit payload 010110, encoded the same way: state the transmitted bit count, the overhead as both an added-bit count and a percentage, and how many single-bit errors the whole 18-bit codeword can guarantee to correct (one per triplet, six triplets).

Evaluate — 30 minutes#

Write your overhead table (see Deposit) and one paragraph: does more redundancy remove the risk of a wrong-but-confident decode, or does it only move the number of errors needed to produce one? Use the failure row above as your evidence.

Deposit — 30 minutes#

Deposit an overhead table with one row per case you worked (the worked example, the check, the protected example, and your 6-bit calculation), columns: payload bits, transmitted bits, overhead, errors corrected per triplet, and the failure case’s error count. Add one line naming the fictional fixture: introduce The Lossless Argument and one sample costing line — for a fictional 100 GB collection at a labelled fictional storage rate of $0.02 per GB per month, 3x repetition raises storage from 100 GB to 300 GB, and the fictional monthly cost from $2.00 to $6.00. State plainly that this cost buys tolerance for one bit-flip per triplet, not protection from every preservation risk. Deposit into the bits collection.

Accessible route#

Labelled text blocks worked by hand; no implementation required. Every bitstring above is plain text, majority vote is arithmetic you can do without a calculator, and the overhead calculation is addition and one division.

Assessment#

The Lossless Argument uses this week’s overhead framework directly in its costing and feasibility criterion (25%): whatever you propose to preserve without loss, state the redundancy scheme, its overhead, and — following today’s failure row — the specific error pattern it does not protect against.