DNA Data Storage: Redundancy & Majority-Vote Decoding

Payload

Message size 8 bytes

Physical Redundancy

Copies per base (R)

Synthesis/read error rate p 4%

Encoded Sequence

— press New Random Message —

Bits encoded

Density (bits/base)

0.00

Theory decode success

0.0%

Bases recovered

—

How it works

Each DNA base (A/C/G/T) encodes 2 bits (log₂4), so one byte maps to 4 bases:

00→A  01→C  10→G  11→T
raw density = 2 bits / base

Real DNA synthesis is error-prone, so a payload is written as R independent physical copies of the same sequence. Each copy suffers random per-base substitution errors at rate p. Decoding takes a majority vote across the R reads at every position:

effective density = 2 / R  bits / base
P(base correct) ≈ Σ_{k=0}^{floor((R-1)/2)} C(R,k)·p^k·(1-p)^(R-k)
P(whole message correct) ≈ P(base correct)^(number of bases)

Message size — payload length in bytes; each byte becomes 4 bases.
R (copies) — how many redundant molecules are synthesized per base position. Higher R buys reliability at the direct cost of storage density.
Error rate p — probability any single physical base is misread during synthesis + sequencing (real DNA storage runs ≈0.5–5%).
Synthesize & Sequence — draws random errors on every copy, then majority-votes each position back to a decoded strand: green spheres matched the original base, red spheres are residual errors the vote could not fix.

This is the actual physical trade-off behind DNA data storage research (Microsoft/UW, Twist Bioscience, Catalog DNA): DNA holds ~215 petabytes/gram in principle, but every real system spends bases on redundancy and error-correcting codes to survive synthesis and sequencing noise.

A C G T

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