HW3_soln

# HW3_soln - EE 568 Homework Solution 1 EE568 Homework...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE 568 Homework Solution 1 EE568 Homework Solution 3 Problem 2.2 The BSC capacity curve was obtained in problem 1.7, and the capacity curve of the BPSK-AWGN channel is available from either from running the FEC-limits program or using the pre-computed curves. Note that the capacity plotted in problem 1.7 was in units of bits per BSC channel use. These two curves are plotted together in Fig. 1 along with their difference. Thus, information theory predicts that soft-in decoding provides and additional coding gain of nearly 2 dB at lower code rates and approximately 1 dB at very high code rates.-2-1 1 2 3 4 5 6 7 8 9 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E b /N (dB) Capacity = Bits Per Channel Use Capacity BPSK vs BSC 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Capacity: Bits Per Channel Use ∆ E b /N o (dB) Difference in Required Eb/No (dB) for BPSK and BSC capacity BPSK (soft input) BSC (hard input) Numerical Precision Error Soft-Input has more potential for greater capacity at a given Eb/No since it contains more "information" relative to the BSC (hard-input). Figure 1: Comparison of capacity for the BPSK-AWGN channel with real observations and the BSC. For the case of 3-bit quantization considered in problem 2.1, the SIR for the resulting DMC can be computed in terms of p ( j | i ) = Pr { output = j | input = i } and p ( i ) = Pr { input = i } : SIR = 1 2 +3 X j =- 4 p ( j | 0) log 2 p ( j | 0) p ( j | 0) + p ( j | 1) + p ( j | 1) log 2 p ( j | 1) p ( j | 0) + p ( j | 1) (1) The transition probabilities p ( j | i ) are given as a function of E c /N in the solution to problem 8. Once this SIR value is computed for a specific E c /N value, we can convert to the minimum value of E b /N via E b /N = 1 SIR E c /N . Not that the units of SIR are bits per channel use (corresponding to a single 1-D BPSK channel use). EE 568 Homework Solution 2-2-1 1 2 3 4 5 6 7 8 9 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E b /N (dB) Capacity = Bits Per Channel Use Capacity BPSK vs DMC (3-bit Quant) vs BSC BPSK (soft input) DMC: Quant 3 bits BSC (hard input) Discrete Memoryless Channel (DMC) 3-bit Quantization performs within 0.2 dB to BPSK Binary Symmetric Channel (DMC with 1-bit quant) performs appx 2 dB degradation relative to BPSK (infinite quantization) Figure 2: Comparison of capacity for the BPSK-AWGN channel with real observations, 3-bit quantization, and 1-bit quantization (the BSC)....
View Full Document

## This note was uploaded on 02/27/2008 for the course EE 568 taught by Professor Chugg during the Fall '07 term at USC.

### Page1 / 7

HW3_soln - EE 568 Homework Solution 1 EE568 Homework...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online