Q3Digital Communication

(a) Classification of Line Encoding Techniques

Line encoding (line coding) techniques, used to represent digital binary data as electrical pulse waveforms suitable for baseband transmission, are classified hierarchically into three main polarity categories, each further divided into Non-Return-to-Zero (NRZ) and Return-to-Zero (RZ) sub-variants based on whether the pulse returns to a zero-voltage level before the end of each bit interval.

• Unipolar: uses only one polarity of voltage (e.g., +V for binary 1, 0V for binary 0) — sub-variants include Unipolar NRZ (pulse remains at +V for the entire bit duration for a '1') and Unipolar RZ (pulse returns to 0V partway through the bit duration for a '1').
• Polar: uses both positive and negative voltage levels (e.g., +V for binary 1, -V for binary 0) — sub-variants include Polar NRZ and Polar RZ.
• Bipolar (pseudoternary): uses three voltage levels (+V, 0, -V), typically representing binary 0 as 0V and alternating the polarity of successive binary 1 pulses between +V and -V — the most common bipolar scheme is Alternate Mark Inversion (AMI), available in both NRZ and RZ variants.

Comparison of Unipolar NRZ, Bipolar RZ, and Bipolar AMI-RZ

Unipolar NRZ: simplest to generate and detect, but suffers from significant disadvantages: it contains a substantial DC component (since the average voltage is non-zero whenever the data has an unequal proportion of 1s and 0s), which cannot pass through AC-coupled (transformer-coupled) transmission lines/repeaters commonly used in communication channels; it provides no inherent timing/synchronization information during long runs of consecutive identical bits (no transitions occur, making receiver clock recovery difficult); and it has no built-in error-detection capability.

Bipolar RZ: by returning to zero within each bit period, RZ formats guarantee at least one transition per bit interval for non-zero bits, substantially improving the receiver's ability to recover timing/synchronization from the received waveform compared to NRZ formats; however, a plain bipolar (polar) RZ format (without the AMI alternation rule) still generally has more bandwidth requirement than NRZ (due to the additional transitions) and, if not additionally alternating with each successive 1, may still retain a DC component depending on the specific data pattern.

Bipolar AMI-RZ (Alternate Mark Inversion, Return-to-Zero): represents binary 0 as 0V (no pulse) and successive binary 1s ('marks') as alternating +V and -V pulses (each returning to zero within the bit period) — this alternation ensures the format has zero DC component regardless of the specific data pattern (since positive and negative mark pulses always balance out over any run of consecutive 1s), and additionally provides simple, built-in error-detection capability: since consecutive marks must always alternate polarity by design, if two consecutive marks are received with the same polarity, this immediately signals that at least one bit error (a 'bipolar violation') has occurred somewhere in the received sequence, without requiring any additional error-detection coding overhead.

Overall comparison: unipolar NRZ, though simplest, suffers from DC content, poor synchronization for long identical-bit runs, and no error-detection capability, making it generally unsuitable for practical long-distance digital transmission; bipolar RZ improves synchronization through guaranteed transitions but does not inherently address DC content or provide error detection unless combined with the AMI alternation rule; and bipolar AMI-RZ combines the synchronization benefits of RZ pulse shaping with zero DC content and simple built-in error detection via the bipolar-violation principle, making it one of the most widely used practical line codes for baseband digital transmission (notably used in the classic T1/E1 digital telephone trunk line standards) despite requiring a somewhat more complex three-level (rather than simple two-level) transmitter/receiver design than the unipolar or polar alternatives.

(b) Quaternary PAM Output Waveform for 0010110111

In a baseband quaternary (4-level) PAM system, each transmitted symbol represents 2 bits (since 2²=4 distinct amplitude levels can represent all 2-bit combinations: 00, 01, 10, 11), with a standard Gray-code-like mapping commonly assigning: 00→-3 (lowest level), 01→-1, 10→+1, 11→+3 (highest level), using natural binary-to-level correspondence with equally-spaced levels (though the specific mapping convention, e.g., Gray coding vs natural binary, may vary by textbook/implementation).

Given input sequence: 0010110111 (10 bits total). Grouping into consecutive pairs (dibits) for quaternary encoding: 00 | 10 | 11 | 01 | 11, giving 5 symbols total (matching the expectation that 10 bits ÷ 2 bits/symbol = 5 symbols).

Mapping each dibit to its corresponding PAM amplitude level (using the convention 00→-3, 01→-1, 10→+1, 11→+3): dibit 00 → level -3; dibit 10 → level +1; dibit 11 → level +3; dibit 01 → level -1; dibit 11 → level +3.

The resulting output waveform consists of 5 successive amplitude levels: -3, +1, +3, -1, +3 (each held constant for one symbol period, which spans 2 bit periods of the original binary sequence), illustrating how quaternary PAM achieves twice the data throughput per symbol compared to binary (2-level) PAM at the same symbol (baud) rate, at the cost of requiring the receiver to reliably distinguish among 4 discrete amplitude levels rather than just 2, making quaternary PAM more susceptible to noise-induced detection errors for a given transmit power level compared to binary PAM, a standard trade-off between bandwidth efficiency (bits per symbol) and noise immunity in M-ary baseband transmission system design.

Verification of the Dibit Grouping and Alternative Mapping Conventions

It is worth double-checking the dibit grouping explicitly: the given 10-bit sequence is 0,0,1,0,1,1,0,1,1,1. Reading strictly left to right in non-overlapping pairs gives (0,0),(1,0),(1,1),(0,1),(1,1), i.e., 00, 10, 11, 01, 11 — exactly the five dibits used above, confirming no bits were dropped or misgrouped in the process. Since 10 is an even number of bits, the grouping divides exactly into 5 whole dibits with no leftover bit, which would not be the case for an odd-length input sequence (in which case a padding convention, such as appending a trailing zero, would need to be specified before quaternary encoding could proceed).

It is also worth noting that the specific dibit-to-level mapping convention (00→-3, 01→-1, 10→+1, 11→+3, used above) is a natural-binary-order mapping, but many textbooks and practical M-ary PAM/QAM systems instead use a Gray-coded mapping (e.g., 00→-3, 01→-1, 11→+1, 10→+3) specifically so that any two amplitude levels that are adjacent to each other in the signal space differ in only a single bit position. This Gray-coding choice is significant for error-rate performance: since the most likely detection error in the presence of noise is a decision that lands on the immediately adjacent amplitude level (rather than a level two or three steps away), Gray coding ensures that this most-probable type of symbol error also corresponds to the least-costly type of error in terms of bit errors — namely, exactly one bit error per symbol error, rather than two. The final waveform shape (the specific sequence of physical amplitude levels transmitted) is unaffected by which bit-to-level convention is used, provided the same fixed mapping convention is applied consistently by both transmitter and receiver, but the resulting bit-error-rate performance under noise is materially better with a Gray-coded mapping than with the natural-binary mapping used in this derivation.

Finally, this problem highlights a broader theme in baseband line coding: the symbol rate (baud rate) of the quaternary PAM waveform here is only half of the underlying bit rate, since each transmitted symbol/pulse now carries 2 bits' worth of information rather than 1 — this directly reduces the required channel bandwidth (roughly proportional to the symbol rate rather than the bit rate) by a factor of 2 compared to an equivalent binary (2-level) PAM system carrying the same total bit rate, which is precisely the general motivation for using M-ary (multi-level) baseband signaling schemes whenever available channel bandwidth is the limiting constraint rather than the achievable signal-to-noise ratio, mirroring the same fundamental bandwidth-vs-noise-immunity trade-off seen later in this paper for M-ary PSK and QAM passband modulation schemes.