Engineer Information Communications cheat sheet

Shannon capacity: C = B·log2(1 + S/N); doubling bandwidth doubles capacity, but capacity grows only logarithmically with SNR (roughly +1 bit/s/Hz per 3 dB when S/N ≫ 1).

Shannon–Hartley uses linear power ratio S/N; converting from dB: S/N = 10^(SNR_dB/10). Eb/N0 = SNR/B·Rb relation links spectral efficiency to energy per bit.

Nyquist sampling: fs ≥ 2·fmax; for a baseband signal of bandwidth B, minimum rate is 2B samples/s, giving 2B independent real symbols per second (B complex symbols/s in passband).

Quantization: SQNR ≈ 6.02n + 1.76 dB for a full-scale sinusoid with n bits; each added bit improves SNR by ~6 dB, and PCM bit rate = fs × n.

Channel capacity with M-ary signaling: theoretical max bits/symbol = log2(M); practical schemes (QAM) sit below the Shannon bound by a coding gap of 1–3 dB.

Entropy H = −Σ p_i log2 p_i bits/symbol; source coding theorem says lossless compression cannot go below H, and Huffman coding achieves within 1 bit of H per symbol.

AWGN error probability decreases exponentially with Eb/N0; BPSK/QPSK BER = Q(√(2Eb/N0)), and QPSK carries 2 bits/symbol in the same bandwidth as BPSK.

Parseval/bandwidth relations: time-bandwidth product B·T counts resolvable degrees of freedom; a pulse of duration T occupies at least ~1/T Hz (Nyquist criterion for zero ISI).

OSI seven layers: Physical, Data Link, Network, Transport, Session, Presentation, Application; TCP/IP collapses to Link, Internet, Transport, Application.

TCP three-way handshake: SYN → SYN-ACK → ACK; connection teardown uses FIN/ACK in each direction, and TIME_WAIT lasts 2×MSL on the active closer.

TCP congestion control: slow start doubles cwnd per RTT until ssthresh, then congestion avoidance adds ~1 MSS per RTT; loss triggers fast retransmit on 3 duplicate ACKs.

IPv4 header is 20 bytes minimum (60 max with options); TTL is decremented per router and dropped at 0; fragmentation uses the 13-bit fragment offset in 8-byte units.

Subnetting: usable hosts = 2^h − 2 for prefix /(32−h); a /26 gives 64 addresses, 62 usable; private ranges are 10/8, 172.16/12, 192.168/16.

NAT/PAT translates private to public addresses using port multiplexing; it breaks end-to-end transparency for inbound connections and embedded IP payloads.

DNS resolution walks root → TLD → authoritative servers; A/AAAA return addresses, CNAME aliases, MX mail exchangers, and TTL controls caching duration.

Ethernet switching learns source MACs into a CAM table and floods unknown unicast; VLAN tags (802.1Q, 12-bit VID) segment broadcast domains; STP prevents L2 loops.

Free-space path loss: FSPL(dB) = 32.44 + 20log10(d_km) + 20log10(f_MHz); received power falls 6 dB per doubling of distance or frequency.

Okumura–Hata and COST-231 models apply for urban macro cells; log-normal shadowing is modeled with a Gaussian dB spread (typically 6–10 dB).

Doppler shift fd = v·fc/c·cosθ; coherence time Tc ≈ 1/(4·fd), and coherence bandwidth Bc ≈ 1/(5·τrms) separates flat from frequency-selective fading.

Rayleigh fading applies without a dominant LOS path; Rician fading with K-factor adds a strong LOS component; diversity order M reduces outage as (SNR)^−M.

OFDM subcarrier spacing Δf = 1/Tu; cyclic prefix length must exceed the channel delay spread to remove ISI, at a cost of CP/Tu spectral efficiency.

Cellular reuse: cluster size N = i² + ij + j², reuse distance D = R·√(3N), and co-channel SIR ≈ (D/R)^γ/6 for a six-interferer first tier.

Link budget: Prx = Ptx + Gtx + Grx − Lpath − Lcable − Lmisc; sensitivity = −174 dBm/Hz + 10log10(B) + NF + required SNR.

4G/5G: LTE uses 15 kHz subcarriers and scalable bandwidths to 20 MHz; 5G NR supports FR1 (sub-6 GHz) and FR2 (mmWave), with flexible numerology 2^μ·15 kHz.

Optical fiber windows: 850 nm (multimode LAN), 1310 nm (zero dispersion in standard SMF), 1550 nm (lowest loss, ~0.2 dB/km, EDFA band C).

Attenuation budget: received power = launched power − (fiber loss × length) − connector/splice losses − margin; typical splice 0.1 dB, connector 0.3–0.5 dB.

Dispersion: chromatic dispersion in ps/(nm·km) broadens pulses; dispersion-shifted fiber moves zero-dispersion to 1550 nm; PMD scales as √length.

WDM: DWDM uses 100/50 GHz ITU-T grids around 1550 nm; CWDM uses 20 nm spacing over 1270–1610 nm with lower-cost uncooled lasers.

Nonlinear limits: SPM/XPM from Kerr effect and FWM in DWDM; launch power must be limited, and dispersion management trades OSNR against nonlinear penalty.

SDH/SONET rates: STM-1 = 155.52 Mbit/s, STM-4 = 622.08, STM-16 = 2.488 Gbit/s; OTN ODU0/1/2/3/4 carry 1.25/2.5/10/40/100 G.

OSNR(dB) = 58 + Pout(dBm) − NF(dB) − 10log10(N) for a 0.1 nm reference in a single-span EDFA chain; each amplifier adds noise and reduces OSNR.

Forward error correction: RS(255,239) gives ~6 dB coding gain; coherent 100G uses soft-decision FEC with ~11 dB net coding gain and DSP-based dispersion compensation.

Symmetric ciphers: AES block = 128 bits with 128/192/256-bit keys (10/12/14 rounds); DES uses 56-bit effective key and 64-bit block, superseded by 3DES and AES.

AES modes: ECB leaks patterns (never for multi-block data); CBC needs a random IV; GCM provides authenticated encryption with a tag, resisting tampering.

Public key: RSA security rests on integer factorization, ECC on discrete logarithms; RSA-2048 ≈ ECC-224/256 in strength; key sizes must scale with threat.

Hash functions: SHA-256 outputs 256 bits; collision resistance is ~2^(n/2) by birthday bound; MD5 and SHA-1 are broken for collision resistance.

Digital signature = hash then sign with private key; verification uses the public key and proves integrity, authenticity, and non-repudiation, not confidentiality.

TLS 1.3 handshake completes in one round trip with ephemeral (EC)DHE for forward secrecy; it removes RSA key transport and static DH, and encrypts most handshake data.

PKI: X.509 certificate binds identity to public key, signed by a CA; validation checks signature chain, validity period, key usage, and revocation via CRL or OCSP.

Common attacks: MITM via unauthenticated key exchange, replay without nonces/timestamps, SQL injection via unparameterized input, and side channels via non-constant-time crypto.

Big-O growth order: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ); binary search is O(log n) on sorted data, merge sort O(n log n) worst case.

Stack vs heap: stack frames are LIFO with automatic lifetime; heap allocation is manual/GC-managed, and recursion depth is bounded by stack size.

Pass by value copies the argument; pass by reference passes an alias so callee mutations are visible to the caller - key distinction in C++ (&) and Java (object references).

TCP socket API sequence: socket → bind → listen → accept (server) and socket → connect (client); close/graceful shutdown uses shutdown or FIN semantics.

Concurrency hazards: race conditions from unsynchronized shared state, deadlock from circular lock acquisition, livelock and starvation; mutex ordering prevents deadlock.

SQL: ACID properties (Atomicity, Consistency, Isolation, Durability); isolation levels READ COMMITTED vs REPEATABLE READ differ on non-repeatable reads and phantom rows.

Version control: git commit creates an immutable snapshot; branch is a movable pointer; merge vs rebase differ in history rewriting and shared-branch safety.

Testing levels: unit (isolated function), integration (module boundaries), system/end-to-end, and regression; code coverage is a necessary but not sufficient quality signal.

ITU structure: ITU-T (standards, formerly CCITT), ITU-R (radio/spectrum), ITU-D (development); Recommendations such as G.652 (SMF) and G.709 (OTN) are voluntary until nationally adopted.

IEEE 802 families: 802.3 Ethernet, 802.11 WLAN, 802.15 WPAN, 802.16 broadband wireless; 802.1 covers bridging, VLANs, and security (802.1X).

3GPP releases define generations: Rel-8 LTE, Rel-10 LTE-Advanced, Rel-15 5G NR; specifications are numbered 23.xxx (architecture) and 38.xxx (NR radio).

IETF publishes RFCs; standards-track RFCs pass Proposed → Draft → Internet Standard, while many RFCs are informational or experimental.

Radio licensing: spectrum is a national resource; unlicensed ISM bands (2.4 GHz, 5 GHz) impose transmit power and duty-cycle limits, while licensed bands require assignment.

Type approval and conformity: equipment must meet EMC and radio tests; CE (EU), FCC Part 15 (US), and similar regimes govern market access.

Numbering and interconnection rules, universal service obligations, and lawful intercept are typically set by national regulators (e.g., FCC, Ofcom, MIC) under telecom acts.

Data protection: GDPR principles (lawfulness, purpose limitation, minimization, storage limits) and breach notification within 72 hours where required.