EngSci++ · source integrity

Errata, without rewriting history.

This ledger accompanies the immutable 50-page Ma126a facsimile. Locations use the printed footer and the one-indexed PDF page. Corrections here were checked from definitions and rendered source; the historical PDF itself is unchanged.

Status: 20 confirmed mathematical or transcription errors. This is a correction ledger, not a claim that every line outside it has been independently proved.

Confirmed corrections

LocationFacsimile issueCorrection
printed 3
PDF 4		Binomial mass uses a coefficient indexed by k for count x, then counts n negative outcomes.Use C(n,x) px(1−p)n−x; there are n−x negatives.
printed 4
PDF 5		Claims logba = logab.logba = 1/logab for valid bases and a > 0.
printed 6
PDF 7		Joint-entropy expectation and expanded conditional-entropy sum omit minus signs.Use −E log p(X,Y) and −Σxp(x)Σyp(y|x)log p(y|x).
printed 10
PDF 11		A joint-convexity mixture repeats p₁; prose calls mutual information concave in the channel law.The mixture uses p₁ and p₂. For fixed input, mutual information is convex in the channel law; for fixed channel, it is concave in the input law.
printed 12
PDF 13		The collision sum Σp(x)r(x) is labelled as the probability of inequality.For independent draws, Σp(x)r(x) = P(X = X̂).
printed 14
PDF 15		Writes p(Xⁿ) → 2−nH as a convergence claim.−n−1log p(Xⁿ) converges in probability to H. Typical probabilities have that exponential order, not ratio convergence.
printed 15
PDF 16		A typical-set cardinality bound omits cardinality bars.Apply the bound to |Aε(n)|.
printed 17
PDF 18		The D-ary alphabet is reversed; the nonsingularity condition mixes variable names.Use {0,…,D−1} and x₁ ≠ x₂ ⇒ C(x₁) ≠ C(x₂).
printed 20
PDF 21		States n−1H(Xⁿ) = nH(X) for IID symbols.n−1H(Xⁿ) = H(X).
printed 21–22
PDF 22–23		McMillan proof changes D−ℓ to Dℓ and uses a false limit.Retain D−ℓ; the required limit is (kℓmax)1/k → 1.
printed 28
PDF 29		The Markov property conditions on the time index n.Condition on the current state: P(xn+1|x1:n) = P(xn+1|xn).
printed 29
PDF 30		Uses p = Pp while later treating P as row-stochastic.With row vectors and row-stochastic P, use μ = μP.
printed 32
PDF 33		Calls I(X;Y) convex in the input distribution.It is concave in the input distribution for a fixed channel.
printed 36
PDF 37		The decoder returns an error when exactly one jointly typical codeword exists.Decode the unique jointly typical codeword; error if none or more than one exists.
printed 42
PDF 43		Writes h(aX) = h(X) + log a.Use h(aX) = h(X) + log|a| for a ≠ 0.
printed 43
PDF 44		The linear-transform identity gives no condition on A.h(AX) = h(X) + log|det A| requires invertible square A and defined entropies.
printed 43
PDF 44		An entropy-power lower bound is claimed for the MSE of any estimator.False as written: X̂ = X has zero error. The shown argument only bounds variance or constant-estimator error; observation-based estimators need a conditional statement.
printed 44
PDF 45		A bin probability is set exactly equal to f(xᵢ)Δ.The exact mass is the bin integral; f(xᵢ)Δ is an approximation or mean-value representation under conditions.
printed 45
PDF 46		Support inclusion is called sufficient for finite KL divergence.Absolute continuity is necessary, not sufficient; the KL integral may still diverge.
printed 47–48
PDF 48–49		Continuous AEP treats densities as point probabilities and gives the typical density the wrong sign.Typical density is of order 2−nh; typical-set volume is of order 2nh.

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