Channel coding and types of LPC

Channel coding

Channel coding is the process of adding controlled redundancy to the data before transmission so that the receiver can detect and correct errors caused by noise, fading and interference. It lowers the BER for a given SNR (coding gain) at the cost of extra bandwidth or lower data rate. Types: block codes (Hamming, BCH, Reed–Solomon), convolutional codes (Viterbi decoding) and turbo/LDPC codes. In mobile systems it is used with interleaving.

Types of linear predictive coder

All LPC coders model the vocal tract with an all-pole filter 1/A(z), whose ~10 coefficients are found by linear prediction, ŝ(n) = Σ aₖ s(n − k). They differ in how the excitation is produced.

1. Basic LPC vocoder (LPC-10)

• Excitation is a pulse train (voiced) or white noise (unvoiced) chosen by a V/UV decision and pitch detector.
• 2.4 kbps; intelligible but synthetic speech.

2. Multi-pulse excited LPC (MPE-LPC)

• Excitation is a small number of pulses (e.g. 4–8 per 5 ms) whose positions and amplitudes are found by analysis-by-synthesis: the encoder tries pulses and keeps those that minimise the perceptually weighted error.
• No V/UV decision needed; good quality at about 9.6 kbps. GSM RPE-LTP uses regularly spaced pulses (regular pulse excitation).

3. Code-excited LPC (CELP)

• Excitation is chosen from a codebook of stored random (Gaussian) sequences. For each sub-frame the encoder passes every codeword through the synthesis filter (with long-term pitch predictor) and picks the one with least weighted error; only its index and gain are sent.

 [codebook]->(×gain)->[pitch filter]->[1/A(z)]-> s^(n)
                                                  |
 s(n) ---------------------------------(-)<-------+
                    error -> [weighting filter] -> min?

• Good quality at 4.8–8 kbps; used in IS-95 (QCELP), FS-1016 and ACELP in GSM EFR.

4. Residual excited LPC (RELP)

• The prediction residual e(n) = s(n) − ŝ(n) is low-pass filtered, down-sampled and sent as excitation; the receiver regenerates the high-frequency part by spectral folding.
• No pitch detection needed; good quality at about 9.6 kbps.